Question 1: You take a statistics exam. The test is a multiple choice questionnaire comprising 7 independent questions. Each question has 9 possible answers, 3 of which are correct. A student is considered to have answered a question correctly if and only if all 3 correct answers have been selected. You will pass the exam if you answer at least 4 questions correctly. We assume that for each question you randomly choose 3 answers. You answer the first question of the exam by randomly choosing 3 answers. What is the probability that you chose all 3 correct answers?

Brand: MathMaster
Rating: 4.9 (183 reviews)

183

likes

915 views

Answer to a math question Question 1: You take a statistics exam. The test is a multiple choice questionnaire comprising 7 independent questions. Each question has 9 possible answers, 3 of which are correct. A student is considered to have answered a question correctly if and only if all 3 correct answers have been selected. You will pass the exam if you answer at least 4 questions correctly. We assume that for each question you randomly choose 3 answers. You answer the first question of the exam by randomly choosing 3 answers. What is the probability that you chose all 3 correct answers?

$Expert avatar$

Lurline

4.6

108 Answers

Let's calculate the probability of choosing all 3 correct answers on the first question:

The total number of ways to choose 3 answers from 9 possible answers is given by the combination formula:

\text{Total possible ways}=\binom{9}{3}=\frac{9!}{3!\left(9-3\right)!}

The number of ways to choose all 3 correct answers is 1, as there is only one correct combination of 3 answers out of the 9:

\text{Number of correct ways} = 1

Therefore, the probability of choosing all 3 correct answers on the first question is:

\text{Probability}=\dfrac{\text{Number of correct ways}}{\text{Total possible ways}}=\dfrac{1}{\frac{9!}{3!\left(9-3\right)!}}

\text{Probability}=\dfrac{1}{\frac{9!}{3!\left(9-3\right)!}}=\dfrac{1}{84}

\boxed{\text{Probability} = \dfrac{1}{84}}

Frequently asked questions (FAQs)

What is the equation to find the vertices of a hyperbola if the center is (-2,3), semi-major axis is 5, and semi-minor axis is 3?

What is the slope-intercept equation of a line that passes through (-3,7) and has a slope of 2?

What is the number of ways to arrange 5 books on a shelf if 2 of them must be placed together?

New questions in Mathematics

calculate the derivative by the limit definition: f(x) = 6x^3 + 2

Y=-x^2-8x-15 X=-7

What is the coefficient of elasticity of the material that must be placed on the heel of the 10 cm high clog, with a base area of 2 cm² so that it deforms only 2 cm when the force on it will be a maximum of 600 N.

3(2+x)-2(2x+6)=20-4x

Karina has a plot of 5000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used to grow lettuce?

How many kilometers does a person travel in 45 minutes if they move at a rate of 8.3 m/s?

If L (-2, -5) reflected across y = -4. What are the coordinates of L?

Determine the equations of the recipes that pass through the following pairs of points P1 (2;-1) and p2 (4;-1)

Derivative of x squared

Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.

Which of the following is the product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths?

Suppose 56% of politicians are lawyers if a random sample of size 564 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportions buy more than 4% round your answer to four decimal places

224 × (6÷8)

The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers

A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.

If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.

What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.

A circular window has a rubber molding around the edge. If the window has a radius of 250 mm, how long is the piece of molding that is required ? (To the nearest mm)

nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north

7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?

You might be interested in