Question

PLEASE PLEEAASE HELP!! You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly? Type your answer below using complete sentences,

Answer 1

The number of ways to permute three correct answers among five questions is 5Choose3 which is 5!/(3!*2!) which equals 10. We must then have the correct answer three times which happens .25 of the time, and two wrong answers 75 of the time. So the probability is 10*0.25^3*.75^2 which is 0.087890625 or roughly an 8.8% chance.