Problem 16. (8 points) Ken, Brad, and Watson are competing in a Jeopardy match.
ID: 3146885 • Letter: P
Question
Problem 16. (8 points) Ken, Brad, and Watson are competing in a Jeopardy match. In Jeopardy!, a question is asked to three contestants, and the contestants have five seconds to answer it correctly. For simplicity, in this problem we will assume that if one contestant answers it incorrectly, then no other contestant can attempt to answer it (ie. at most one person can attempt to answer each question). When each contestant attempts to answer, they have the following probabilities of answering correctly: Ken: 0.8 | Brad: 0.7 Watson: 0.9 (i) Of the total questions in this match, 20% are attempted by Ken (correctly or incor- rectly), 30% are attempted by Brad, 30% are attempted to be answered by Watson, and 20% are not attempted by any of the contestants. Given that a question was answered correctly, what is the probability that it was answered by Ken? (ii) Now suppose that of the total questions, Ken knows the answer to 40% of them. Using answer the given probabilities from part A, what is the probability that he attempts to given he knows the answer to the question?Explanation / Answer
P(C|K) = 0.8, P(C|B) = 0.7 and P(C|W) = 0.9
i)
Probability that question was answered correctly,
P(C) = 0.2*0.8 + 0.3*0.7 + 0.3*0.9 = 0.64
Required probability, P(K|C) = P(C|K)*P(K)/P(C)
= 0.2*0.8 / 0.64
= 0.25
ii)
Ken knows answers to the question, P(K) = 0.4
P(A|K) = 0.4*0.2/0.4 = 0.2