A student takes an exam containing 10 multiple choice questions. The probability of choosing a correct answer by knowledgeable guessing is 0.2. At least 6 correct answers are required to pass. If the student makes knowledgeable guesses, what is the probability that he will fail? Round your answer to four decimal places.

0.9936 is the probability that the student will fail.

Step-by-step explanation:

We are given the following information:

We treat adult guessing correct answer as a success.

P(guess correct answer) = 0.2

Then the number of correct guesses follows a binomial distribution, where

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 = 10

The student needs atleast 6 correct answer to pass the test. We have to calculate the probability that the student will fail.

We have to evaluate:

0.9936 is the probability that the student will fail.