# Suppose a multiple choice test contains 30 questions. If each question has 5 answer choices only one of which is correct, what is the expected number of questions to be answered correctly by guessing?  The SAT used to penalize wrong answers by subtracting 1/4 a point from each incorrect answer. If each question on the SAT has 5 answer choices only one of which is correct, what is the expected number of points awarded by guessing on 30 questions?

Question

Suppose a multiple choice test contains 30 questions. If each question has 5 answer choices only one of which is correct, what is the expected number of questions to be answered correctly by guessing?

The SAT used to penalize wrong answers by subtracting 1/4 a point from each incorrect answer. If each question on the SAT has 5 answer choices only one of which is correct, what is the expected number of points awarded by guessing on 30 questions?

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Step 1

An experiment with two possible outcomes follows the binomial distribution.

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

Step 2

Let X is the number of correct answers, which follows the binomial distribution with parameters n, p.

A multiple choice test contains 30 questions and each question has 5 choices out o...

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