A quiz consists of 25 questions Each question has 5 answer c

A quiz consists of 25 questions. Each question has 5 answer choices with exactly one correct answer. A student is completely unprepared for the quiz, so he guesses on all 25 questions. How many questions should the student expect to answer correctly?

Solution

let X be the random variable denoting the number of questions the student answered correctly

each of 25 questions has 5 answer choices and he guesses all questions

hence the probability of correcting a question is 1/5

so X~Bin(25,1/5)

hence his expected number of correct answers=E[X]=25*1/5=5 [answer]