Question

A student takes a multiple-choice test that has 10 questions. Each question has five choices. The student guesses randomly at each answer. 1. Find P(2) 2. P (more than 3)

Answer 1

Each question has five choices. Since the student guesses randomly at each answer, and only one of the 5 is correct, the probability that the student guesses the correct answer on any given question is 1/5=0.20

Let X be the number of questions out of 10 which are answered correctly. We can say that X has a binomial distribution with parameters, number of trials (number of questions in the test) n=10 and success probability ( the probability that the student guesses the correct answer on any given question ) p=0.20

The probability of getting X=x correct is

1. Find P(2)

ans: P(2) = 0.3020

2. P (more than 3)

ans: P(more than 3) =0.1209