Question

Richard has been given an 11-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 11 questions, find the probability that he will answer at least 4 questions correctly. Round your answer to the nearest thousandth. a. 0.111 b. 0.161 c. 0.364 d. 0.073 e. 0.5

Answer 1

Option b) 0.161

Explanation:

We are given the following information:

We treat correct as a success.

P(Correct Answer) =
`(1)/(5)` = 0.2

Then the number of questions follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 11

We have to evaluate:

P(answer at least 4 questions correctly)

`P(x \geq 4)\\=1 - P(x = 0) - P(x = 1) - P(x = 2) - P(x = 3)\\=1 - \binom{11}{0}(0.2)^0(1-0.2)^(11) - ... - \binom{11}{3}(0.2)^3(1-0.2)^(8)\\=1 -0.085 -0.237-0.296 - 0.221\\= 0.161`

Thus, 0.161 is the probability that Richard will answer at least 4 questions correctly.

Option b) 0.161