A multiple-choice quiz consists of 5 independent questions
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A multiple-choice quiz consists of 5 independent questions. Each question has 4 options with exactly one correct answer. A student, who has not studied, guesses the answer to every question at random. Let C be the event "the student answers at least one question correctly". Work out the following:
(i) Determine the probability that the student answers none of the questions correctly.
(ii) Using the result from part (i), find P(C).
(iii) If the quiz were to contain 8 such independent questions instead of 5, how would the probability in part (ii) change? Calculate the new probability that the student answers at least one question correctly.