8. Pat is a student taking an economics course. Pat\'s exam strategy is to rely

Question

8. Pat is a student taking an economics course. Pat's exam strategy is to rely on luck for the next quiz. The quiz consists of n multiple-choice questions. Each question has four possible answers, only one of which is correct. Pat plans to guess the answer to each question without reading it. Assume that each question is independent of each other. If a grade on the quiz is more than 50%, Pat will pass the quiz. a. When n-10, find the probability that Pat will pass the quiz. b. When n- 20, find the probability that Pat will pass the quiz. c. When n-100, find the probability that Pat will pass the quiz.

Explanation / Answer

We will use the binomial

Let p be the probability that guess is right =1/4 =0.25 and q of not getting the guess right.

The student will pass if he gets 5 or more guess right

Let X be the number guesses.

P(pat will pass) = p(X>=5)

=1-P(X<=5). Using binomial table to find the probability.

For n =10 .

Probability that Pat will pass = 1-0.9219 = 0.078

Similarly we will find for n = 20 nd n=100.

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