Question

A student takes an exam containing 18 true or false questions, if the students guesses, what is the probability that he will get less than 10 but more than 7 questions right

Answer 1

0.3523 is the probability that the student will get less than 10 but more than 7 questions right.

Explanation:

We are given the following information:

We treat answering the question correctly as a success.

P(guess of answer is correct) = 50% = 0.5

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 = 18

We have to evaluate:

`P(7 < x < 10) \\= P(x = 8) + P(x = 9) \\= \binom{18}{8}(0.50)^8(1-0.50)^(10) + \binom{18}{9}(0.50)^9(1-0.50)^9\\= 0.1669 + 0.1854\\= 0.3523`

0.3523 is the probability that the student will get less than 10 but more than 7 questions right.