Question

A multiple choice test contains 35 questions on it with five possible answers on each question. Assuming a student has not attended class and has no knowledge of the material and must choose randomly between the answer choices, find the probability that the student gets 6 questions correct. Round your answer to 4 decimal places. Using a statistic calculator.

Answer 1

0.1558

Explanation:

To solve this problem we are going to use the Binomial distribution.

The probability of guessing correctly is: 1/5 = 0.20.

Therefore the probability of guessing incorrectly is: 1 - 1/5 = 0.80.

The total number of trials is 35 (because the test has 35 questions)

And we're looking for 6 successes and 29 failures.

The problem asks us what is the probability that the student gets 6 questions correct. This would be:

`P(6)= C_(35|6)(0.20)^(6)(0.80)^(29)\\P(6)=1623160(0.000064)(0.0015)\\P(6)=0.1558`

Thus, the probability of getting 6 questions correct is 0.1558