Question

A student has to take two quizzes tomorrow. He has only enough time to study for one of them. The history quiz has 5 true or false questions. The science quiz has 3 multiple choice questions. The student calculates the probability that he will get all the questions correct by guessing. The student will study for the quiz on which he is likely to do worse by guessing. Which quiz should he study for?
A. History, because he must get more questions correct.

B. Science, because the probability of getting all the questions correct is 0.016, which is lower than for history (0.031).

C. History, because the probability of getting all questions correct is 0.031, which is lower than for science (0.75).

D. Science, because the probability of getting all questions correct is 0.075, which is lower than for history (0.25).

Answer 1

Answer: option B

Step-by-step explanation:

Miguel has to take two quizzes

1) 4 true or false questions on History with a 0.5 chance of acing the quiz

Expected number of correct questions = np

n = number of questions

p = probability of acing the test

Expected number of correct questions = 4 × 0.5 = 2

2) 3 multiple choice questions on Science with a 0.2 chance of acing the quiz.

Expected number of correct questions = 0.2 × 3 = 0.6

It is evident that guessing would yield a worse result in the Science quiz with less than 1 question expected to be correct than history, where he is still expected to get 2 questions correctly by guessing.