MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
A multiple-choice quiz consists of 6 questions, each having exactly four options with one correct answer. A student answers every question by random guessing, and different questions are answered independently. Using this information, answer the following:
(i) Find the probability that the student answers all six questions correctly.
(ii) Find the probability that the student answers the first, third and fourth questions correctly and the remaining questions wrongly, in that specified order.
(iii) Find the probability that the student gets exactly three correct answers in the quiz.
(iv) Ten such students attempt the same quiz independently. Find the probability that at least one of them answers all six questions correctly.