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 unit vector in the direction of vector v=?

What is the value of cos(π/6) - sin(π/4) + tan(3π/8)?

What is the product of a mixed number, 3 and 1/4, and a factored number, 2^3 × 5²?

New questions in Mathematics

A particular employee arrives at work sometime between 8:00 a.m. and 8:40 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:40 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:30 a.m. Round your answer to four decimal places, if necessary.

Since one of the three integers whose product is (-60) is (+4), write the values that two integers can take.

Use the digits of 1,9,2,3 to come up with all the numbers 98 and 95

Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.

How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.

Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6

A study reports the following final notation: F (3, 32) = 9.50, p < .05. How many total participants were involved in this study? Group of answer choices 34 32 36

Calculate the minimum size of a simple random sample assuming a sampling error of 5% assuming that the population size is 100 elements

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.2 in. Find P95. That is, find the hip breadth for men that separates the smallest 95% from the largest 5%.

The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?

Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.

Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.

Find sup { x∈R, x²+3<4x }. Justify the answer

Log0

P 13. Let P a point inside of a square ABCD. Show that the perpendicular lines drawn from A, B, C, respectively D, to BP, CP, DP, respectively AP are concurrent. Use geometric rotation.

A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?

4m - 3t + 7 = 16

Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?

The following incoming payments show up at a tax inspection: 25 000€ on 19.01.2008, 140 000€ on 27.03.2008 and 19 000€ on a date that which is illegible, and 60 000€ on 15.06.2008. On which date did the payment of the 19 000€ appear, if on 30.06.2008 the money on the account (incl. interest at 4%) is 246 088.89€? Use simple interest and 30E/360 DCC. Solution: 45 days, 15.05.08

Sin(5pi/3)

You might be interested in