Question

A student takes an exam containing 13 true or false questions. At least 9 correct answers are required to pass. If the student guesses, what is the probability that he will pass? Round your answer to four decimal places.

Answer 1

Since, the student guesses each question, and there are two options (true or false) for each question, the probability that he guesses correctly on a question, p = 1/2.

Now, let X denote the random variable representing the number of correct answers (out of 13) of the student on the exam.

Now, since there is a fixed number of questions (13), each question has two possible outcomes (correct or incorrect) and each question is answered correctly with probability p = 1/2 independent of other questions. Thus, we can conclude that:

X ~ Bin(n=13, p=1/2)

Thus, the probability mass function of X is given by:

Now, for the student to pass, he needs to correctly answer at least 9 questions. Thus, the probability that the student will pass is given by:

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