Question

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.

Answer 1

Answer:

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

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

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 = 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:

$P(x < 6) =1 -( P(x = 6)+...+ P(x = 10) )\\\\=1-( \binom{10}{6}(0.2)^6(1-0.2)^4 +...+ \binom{10}{10}(0.2)^{10}(1-0.2)^0)\\\\=1- 0.0064=0.9936$

0.9936 is the probability that the student will fail.