Question

: Suppose you are given a 3 question multiple-choice test. Each question has 4 responses and only one is correct. Suppose you want to find the probability that you can just guess at the answers and get 2 questions right. (Teachers do this all the time when they make up a multiple-choice test to see if students can still pass without studying. In most cases the students can't.) To help with the idea that you are going to guess, suppose the test is in Martian.

Previous question

Answer 1

Explanation:

This is a binomial probability problem. You have n = 3 independent trials (the 3 questions on the test), and the probability of success on each trial (guessing the correct answer) is p = 1/4 (since there are 4 possible answers and only one is correct). You want to find the probability of k = 2 successes (getting 2 questions right).

The binomial probability formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Plugging in the values for this problem, we get:

P(X = 2) = (3 choose 2) * (1/4)^2 * (3/4)^(3-2) = 3 * (1/16) * (3/4) = 9/64

So the probability of guessing at the answers and getting 2 questions right on a 3 question multiple-choice test with 4 responses per question is 9/64.