On the planet Kudzu, the probability that an animal is blue is 0.20. The probability that the animal is blue given that the animal is female is 0.20. Which statement is true
Answers
On Kudzu, being female and being blue are independent events.
We have given that,
The probability that an animal is blue is 0.20.
We have to determine,
Which statement is true.
What is the probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Therefore the correct statement is,
On Kudzu, being female and being blue are independent events.
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Related Questions
the accompanying major league baseball data provide data for one season. use the data to build a multiple regression model that predicts the number of wins. complete parts a through c.
Answers
Considering the data we have been provided, we can build a multiple regression model as follows.
a.) In MS Excel, we enter the data set and utilize the "Correlation" option under Data > Data Analysis to create the correlation matrix and answer the question. The correlation matrix may be seen below.
[Fig. 1]
Correlation coefficients for at least one of the independent variables are larger than 0.7.
b.) We must look at the column labeled "Won" in the correlation matrix. The variables are Runs, Hits, Earned Run Average (ERA) and Walks if the criteria are 0.4.
c.) In MS Excel, we enter the data set and utilize the "Regression" option under Data > Data Analysis to create the regression model and answer the question. The result is shown below.
[Fig. 2,3,4]
Runs, ERA, and SO are all significant, with p-values less than 0.05. As a result, we recreate the regression model with these three independent variables.
[Fig. 5,6,7]
The right answer is Won = 80.321 + (0.101) X1 + (-14.276) X3 + (-0.011) X4.
The R2 value of the model is 0.948. This suggests that these factors can predict 94.8% of the number of victories. This model does not make use of the same variables as the previous one (b).
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which of the following are solutions to the equation sin x cos x= -1/4
Answers
Answer:
x=-pie/12
sinxcosx=-1/4
multiply both sides by 2
sin2x = 2sinxcosx we know
now equation will be
sin2x = -1/2
2x=-pie/6
x=-pie/12
To express the polynomial 4a^3 + a^2 - 6a^5 + 2a^3 - 4a + 1 in standard form, which terms should be combined?
Answers
Answer:
Step-by-step explanation:
-6a^5+6a^3+a^2-4a+1
Answer:
4a^3 and 2a^3
Step-by-step explanation:
you always start by combining like terms
In professor Hoepker's class, there are X tests and a final. At the end of the semester, the lowest Y test scores are dropped and the remaining test scores and the final (which has twice the weight of a test) are averaged to compute the average score for the entire class. The final cannot be dropped. Going into the final, student Kaytee has an average of W on the X tests. The sum of her lowest Y test scores is L. Her final exam score is S. Find her average score G in the class in terms of X, Y, W, L, and S.
Answers
Step-by-step explanation:
Kaytee's total points are WX + 2S − L. The total number of exams is W − Y + 2. Therefore:
G = (WX + 2S − L) / (X − Y + 2)
The total number of exams is W − Y + 2.
We have given that,
In professor Hoepker's class, there are X tests and a final. At the end of the semester, the lowest Y test scores are dropped and the remaining test scores and the final (which has twice the weight of a test) are averaged to compute the average score for the entire class. The final cannot be dropped.
Going into the final, student Kaytee has an average of W on the X tests. The sum of her lowest Y test scores is L. Her final exam score is S.
What is the sum?The sum brings two or more numbers together to make a new total.
We have to determine her average score of G in the class in terms of X, Y, W, L, and S.
Kaytee's total points are WX + 2S − L.
The total number of exams is W − Y + 2.
Therefore:G = (WX + 2S − L) / (X − Y + 2)
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A graphing calculator is recommended. Use technology to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. (Round your answers to five decimal places.) y = e−x2, y = 0, x = −5, x = 5. a) about x-axis. b) about y= - 1
Answers
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740
We have to find the volume of given curve about x-axis
we have \($\mathrm{y}=\mathrm{e}-\mathrm{x}^2,\) y=0, x=-5, x=5
(a).
The volume of solid of revolution about the x-axis using disk method is evaluated as:
The disk method is the process of finding the volume of an object by dividing that object into many small cylinders/disks and then adding the volumes of these small disks together.Volume V=\(\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$\)
\($$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$\)
V=3.93740
we use the formula
\($$\int_{-\mathrm{n}}^{\mathrm{n}} \mathrm{e}^{-\mathrm{a} \mathrm{x}^2} \mathrm{dx}=\frac{\sqrt{\pi} erf \sqrt{a} n }{\sqrt{a} }\)(b). The volume of solid of revolution about the y= - using washer method is:
This particular shape is called a washer, or a disk. This shape is obtained by rotating two functions around the x-axis or the y-axis. To find the volume of this shape, create slices of the shape and subtract the missing middle space after finding the total volume. This method is called the washer method.\($$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$\)
Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740
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there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
Answers
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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A car rental costs $50 per day plus an additional $0.20 for each mile driven. The daily cost y is given by the equation
y = 0.20x + 50
where x is the number of miles driven. Find the y-intercept of the graph of the equation.
(x, y) =
Answers
Answer:
(0, 50)
Step-by-step explanation:
The y-intercept is when x=0.
\(y=0.20(0)+50=50\)
A specimen of 100 mm length along the stroke of a shaper is machined with 15° rake angle tool. Determine the shear plane angle and chip thickness if uncut chip thickness is 1.5 mm and chip length obtained is 40 mm.
Answers
The shear plane angle is approximately 84.3°, and the chip thickness is approximately 15.1 mm.
What is the shear plane angle?To determine the shear plane angle and chip thickness in the given scenario, we can use the following formulas:
Shear Plane Angle (α):
tan(α) = tan(β - φ)
where β is the inclination angle of the machined surface (rake angle) and φ is the friction angle.
Chip Thickness (t):
t = tc / cos(α)
where tc is the uncut chip thickness.
Given:
Uncut chip thickness (tc) = 1.5 mm
Chip length (lc) = 40 mm
Length of the specimen (L) = 100 mm
Rake angle (β) = 15°
First, we need to calculate the shear plane angle (α):
tan(α) = tan(β - φ)
Since the friction angle (φ) is not given, we will assume a typical value of 5°.
tan(α) = tan(15° - 5°)
tan(α) = tan(10°)
α ≈ 84.3° (rounded to two decimal places)
Next, we can calculate the chip thickness (t):
t = tc / cos(α)
t = 1.5 mm / cos(84.3°)
t ≈ 15.1 mm (rounded to two decimal places)
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Which table represents the statement "Di runs at a rate of 4 meters per second " ?
Answers
Answer:
d=4t
Step-by-step explanation:
Patricia buys a round
dinner table that has a
diameter of 12 meters. What
is the area of the table?
Answers
Answer:
A = 113.1 (rounded to the nearest tenth)
Step-by-step explanation:
A = \(\pi r^{2}\)
Diameter is 12, so the radius is 6
\(\pi\)(6)^2
36\(\pi\) ≈ 113.0973355
113.1 (rounded to the nearest tenth)
Part 1 - Application
Eden is working on an experiment for her science fair project. She is planting a total of 24 herbs for an herb garden. She is going to plant basil and mint. The basil plants cost $.25 per plant and the mint plants cost $.50 per plant. Eden has a total of $10 to spend on plants because she also has to purchase potting soil and a long planter pot. Write a system of equations and solve either using elimination or substitution. Be sure to identify your variables.
Answers
Eden should purchase 8 basil plants and 16 mint plants to stay within her budget of $10.
What is a system of equations?
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given that;
Number of herbs=24
Cost of basil plant= 0.25
Cost of mint plant=0.50
Eden has $10
Now,
Let's use the variables b and m to represent the number of basil and mint plants that Eden will purchase, respectively. Then, we can write two equations based on the total number of plants and the total cost:
b + m = 24 (the total number of plants is 24)
0.25b + 0.5m = 10 (the total cost of the plants is $10)
To solve this system of equations, we can use substitution. Solve the first equation for one variable in terms of the other:
b = 24 - m
Substitute this expression for b in the second equation:
0.25(24 - m) + 0.5m = 10
Simplify and solve for m:
6 - 0.25m + 0.5m = 10
0.25m = 4
m = 16
Substitute this value of m back into one of the original equations to solve for b:
b + 16 = 24
b = 8
Therefore, the solution of the equations will be 8 and 16.
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Which of the following is the graph of f(x) = 5 cos (2x)? Select one: a. graph with points 0, 5 and pi over 4, 0 and pi over 2, negative 5 and 3 pi over 4, 0 and pi, 5 b. graph with points at 0, 0 and pi over 4, negative 3 and pi over 2, 0 and 3 pi over 4, 3 and pi, 0 c. graph with points 0, negative 5 and pi over 4, 0 and pi over 2, 5 and 3 pi over 4, 0 and pi, negative 5 d. graph with points at 0, 5 and pi over 4, 2 and pi over 2, negative 1 and 3 pi over 4, 2 and pi, 5
Answers
The required graph has been attached below that represents the function f(x) = 5 cos (2x).
The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.
Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.
The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).
Thus, the graph has been attached below that represents the given function.
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the measures of ABD is (0.2x+52) and the measures of CBD is (0.2x+42) find the value of x
Answers
The value of x in the triangle is determined as 45.
What is the value of x?The value of x in the triangle is calculated by applying the following formula,.
The measure of angle ABD = 0.2x + 52
The measure of angle CBD = 0.2x + 42
From the diagram, we can set-up the following equations;
x + 16 = 0.2x + 52
Simplify the equation above, by collecting similar terms;
x - 0.2x = 52 - 16
0.8x = 36
Divide both sides of the equation by " 0.8 "
0.8x / 0.8 = 36/0.8
x = 45
Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.
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A bakery wants to bag at most 100 cookies into cookie packs. Each cookie pack has 4 cookies. They have already bagged 20 cookies. How many more bags of cookies could they make?
Write an inequality describing the situation and solve. Which inequality below is correct?
Answers
They may bake 20 additional bags of cookies. The problem is represented by the inequality x < 80.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, A bakery wants to bag at most 100 cookies into cookie packs. Each cookie pack has 4 cookies. They have already bagged 20 cookies.
Since each cookie pack can hold 4 cookies
Thus, 100 cookies will require = 100/4 packs
100 cookies will required = 25 packs
Since They have already bagged 20 cookies.
Thus,
The total pack they used = 20/4
The total pack they used = 5
Inequality:
let "x" be the number of cookies they can make
80 > x
Therefore, 20 more bags of cookies they could make. the inequality that represents the situation is x< 80.
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PLS HELP DUE VERY SOON
3. Consider the following box plot.
(a) Find the interquartile range.
(b) What percent of values is included in the interquartile range?
Answers
Answer:
a. IQR = 2.25
b. 40%
(I'm not sure about B.)
Step-by-step explanation:
a.=Q3 - Q1
=4.7 - 2.2
=2.5
b. =2/5 × 100/1
=40%
If a loading ramp is placed next to a truck, at a height of 8
feet, and the inclined portion of the ramp is 17 feet long, what angle (in degrees) does the ramp make with the ground?
Round your answer to one-tenth of a degree.
Answers
The angle that the ramp makes with the ground is approximately 28.07 degrees.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):
Sin(θ) = 8/17
We can use a calculator to find the inverse sin of this ratio to get the angle θ:
θ = sin⁻¹(8/17)
θ ≈ 28.07 degrees
Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.
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A. 3/4=a/36
B.4/9=b/36
Answers
Answer:
A. = 27 B. = 16
Step-by-step explanation:
A. 36/4 = 9 3X9 = 27
B. 36/9 = 4 4X4 =16
Charlie the trainer has two solo workout plans that he offers his clients: Plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 6 who did plan B. On Thursday there were 3 clients who did plan A and 2 who did plan B. Charlie trained his Wednesday clients for a total of 7 hours and his Thursday clients for a total of 3 hours. How long does each of the workout plans last?
Answers
Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the System of equations.
To determine the duration of each workout plan, let's assume that both Plan A and Plan B have a fixed duration. Let's denote the duration of Plan A as "x" hours and the duration of Plan B as "y" hours.
From the given information, we can form the following equations:
On Wednesday:
5 clients did Plan A, so the total duration for Plan A is 5x hours.
6 clients did Plan B, so the total duration for Plan B is 6y hours.
The total training duration on Wednesday is 7 hours, so we have the equation: 5x + 6y = 7 ... Equation (1)
On Thursday:
3 clients did Plan A, so the total duration for Plan A is 3x hours.
2 clients did Plan B, so the total duration for Plan B is 2y hours.
The total training duration on Thursday is 3 hours, so we have the equation: 3x + 2y = 3 ... Equation (2)
We now have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.
Multiplying Equation (1) by 2 and Equation (2) by 5 to eliminate the y variable, we get:
10x + 12y = 14 ... Equation (3)
15x + 10y = 15 ... Equation (4)
Multiplying Equation (3) by 3 and Equation (4) by 2 to create a new system of equations:
30x + 36y = 42 ... Equation (5)
30x + 20y = 30 ... Equation (6)
Subtracting Equation (6) from Equation (5), we can eliminate the x variable:
(30x + 36y) - (30x + 20y) = 42 - 30
16y = 12
y = 12/16
y = 0.75
Substituting the value of y into Equation (2), we can solve for x:
3x + 2(0.75) = 3
3x + 1.5 = 3
3x = 3 - 1.5
3x = 1.5
x = 1.5/3
x = 0.5
Therefore, the duration of Plan A is 0.5 hours, and the duration of Plan B is 0.75 hours.
Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the system of equations.
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Consider this function and its graph. f(x) = tan(3x + pi/4) - 1 Which statement best describes function f?
A. The function is odd.
B. The function is even.
C. There is not enough information to determine whether the function is even or odd.
D. The function is neither even nor odd.
Answers
Answer: D. The function is neither even nor odd.
Step-by-step explanation:
A function f(x) is even if:
f(x) = f(-x) for all x-valies
A function f(x) is odd if:
f(x) = -f(-x) for all x-values.
If there is only one value of x such that the above conditions are false, then the function is neither odd nor even.
In the graph, we can see that:
f( -π/3) = f(π/3)
This would imply that the function is even (at least in that point)
And can also see that as x increases from zero, the value of f(x) increases.
And as x decreases from zero, the graph of f(x) decreases.
So for a point 1 > a > 0, we have that:
f(a) ≠ f(-a)
Then we can conclude that the function is neither even nor odd, the correct option is D.
Answer:
D. The function is neither even nor odd
Step-by-step explanation:
edmentum
A total of 803 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53 more student tickets sold than adult tickets How many adult tickets were sold? adult tickets *
Answers
Answer:
375
Step-by-step explanation:
Based on the given conditions, formulate: 53 +2x = 803
Rearrange variables to the left side of the equation:
2x = 803 - 53
Calculate the sum or difference:
2x = 750
Divide both sides of the equation by the coefficient of variable:
x = 750/2
Cross out the common factor: x = 375
fill in the blank. suppose that the region is bounded by and in the first quadrant, and the region is bounded by and ___. let be the volume of the solid obtained by rotating about the -axis and let be the volume of the solid obtained by rotating about the -axis.
Answers
Answer: suppose that the region is bounded by y = x and y = 2x in the first quadrant, and the region is bounded by x = 0 and y = 2. let V_x be the volume of the solid obtained by rotating about the x-axis and let V_y be the volume of the solid obtained by rotating about the y-axis.
Step-by-step explanation:
Find the surface area and volume of a sphere.
A = 4 r²
V = 4/3r³
A sphere has a radius of 4 inches.
Area (to the nearest tenth) =
Volume (to the nearest tenth) =
sq. in.
cu. in.
Answers
\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)
What is the constant and variable of 6a in algebra
Answers
Answer:
Constant is 6 and the variable is a
An artist's canvas has sides measuring 3x + 5 and 2x + 1 inches.
What is the area of the canvas? Show all work.
The artist laid the canvas flat on the floor and poured some paint in the center. The paint flows at a rate of r(t) = 2t where t represents time in minutes and r represents how far the paint is spreading on the canvas. The area of the paint can be expressed as A[r(t)]= rur?. What is the area of the circle created by the paint?
If the artist wants the circle to be at least 300 in?, will it be that large in 5 minutes? Support your answer with your work.
Answers
The area of the circle created by the paint is given by the expression 4πt².
The area of the circle is 100π, which is approximately 314.16 in².
The circle will be at least 300 in² in 5 minutes. Yes.
To find the area of the canvas, we multiply the lengths of its sides:
Area = (3x + 5) × (2x + 1)
Expanding the expression:
Area = 6x² + 3x + 10x + 5
Combining like terms:
Area = 6x² + 13x + 5
The area of the canvas is given by the expression 6x² + 13x + 5.
Now, let's find the area of the circle created by the paint.
The area of a circle is given by the formula A = πr², where r represents the radius.
The radius is given by the spreading of paint, which is r(t) = 2t.
Substituting the value of r(t) into the formula, we have:
A[r(t)] = π(2t)²
Simplifying:
A[r(t)] = π(4t²)
A[r(t)] = 4πt²
Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.
Substitute t = 5 into the area formula:
A[r(5)] = 4π(5)²
A[r(5)] = 4π(25)
A[r(5)] = 100π
Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.
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Find the equation of the parabola with the following properties. Express your answer in standard form.
Symmetric with respect to the line y = 2
Directrix is the line x = 11
P = -3
Answers
The equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1
What is the equation of the parabola?To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.
Alternatively, we can use PF = PM to find the equation of the parabola.
vertex is half way between the focus and directrix
It's a downward opening parabola, general form
y= a(x-h)^2 + k
where (h,k) = vertex= (-3,-1)
plug in another point on the parabola to solve for a which gives
am answer with either x coefficient = -1'/4 or =4 Check the math.
one or the other is right another point is the y intercept = 9a-1
Another point is directly to the right of the focus (-1, -2) It's 2 down from the directrix and 2 to the right of the focus, equidistant. plug that point into y= a(x+3)^2 -1 and solve for "a"
-2 = a((-1+3)^2 -1
-2 = 4a -1
4a = -
a = -1/4
The parabola is y = (-1/4)(x+3)^2 -1
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What is h? even if you can just tell me how to find it would be helpful!
Answers
Answer:
possibly 5?
Step-by-step explanation:
But can you plzzz help me with my latest question
In the expression if 2X=5=8X then 12X= ? you subtract 2X from each sideto get 5=6X then multiply both sides by 2
Why do you multiply both sides by 2
Answers
The value of 12x in the expression is 10
You multiply 5 = 6x by 2 to get 12x
Calculating the value of 12x in the expression
From the question, we have the following parameters that can be used in our computation:
2x + 5 = 8x
You subtract 2X from each side to get
5 = 6x
Then multiply both sides by 2
This gives
10 = 12x
So, we have
12x = 10
Why do you multiply both sides by 2
You multiply by 2 because the question requests for the value of 12x
Since, we have solved for 6x, the next step is to multiply 6x by 2 to get 12x
i.e. 6x * 2 = 12x
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Find the surface area of the Triangular prism.
A = bh
A = 1/2(bh)
Answers
Answer:
Surface area of triangular prism =1/2(bh)
=1/2(3*4)
=6
y > 2x - 1 for (2, 3)
Answers
Answer:
Solution Steps:
Roll one-8 sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by .
Answers
The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.
Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.
Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:
P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)
where:
C (n , k) represents the number of combinations of "n" things taken "k" at a time, and p is the probability of success in a single trial.Step1
Calculate the probability of rolling a seven on an 8-sided die (p).
Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),
p = 1/8.
Step 2
Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:
P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)
On subtracting gives:
=C(10, 3) * (1/8)^3 * (7/8)^{7}
Plugging the value of C(10,3) = 120 in the above equation:
= 120 * (1/8)^3 * (7/8)^{7}
Step 3:
Calculate the final answer using the formula:
P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)
≈ 0.0142
Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.
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