2 Fred is answering a multiple choice question exam Each que

2. Fred is answering a multiple choice question exam. Each question has n possible answers. If Fred knows the correct answer to a question, he always gets it correct; otherwise he takes a guess, picking any answer with equal probability. Let K be the event that Fred knows the answer to a question and let R be the event that Fred answers the question correctly. Given P(K) = 3/4 what is P(R)? Write your answer in the box provided and show any working below.

Solution

P(K) = 3/4

P(R) = P(Fred knows the answer ) + P( Freds guess will go correct)

        = 3/4 * 1 + (1-3/4)(1/n)

= 3/4 + 1/4n

= (3n+1)/4n Answer