Amultiple choice test has 7 questions each of which has 4 possible answers, only one of which is correct. if judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

Each question is a random variable, with probability 1/4 of success (only one answer over four is correct). We repeat this experiment 7 times, hoping to succeed three times.

This is exactly the case where Bernoulli distribution is useless. We use it when we repeat identical experiments times, expecting successes, with a success probability of [/tex] p [/tex] (which implies a failure probability of . That probability is

where the binomial coefficient is defined as

If we plug our values, we have