Question

Alice and Bob took a test, which has ten questions. Given that Alice answered six questions correctly and Bob answered eight questions correctly, compute the probability that there exists at least one question on the test which is answered correctly by Alice but not by Bob.

Answer 1

0.12

Explanation:

Total number of questions in the book = 10

Number of questions answered correctly by Alice = 6

Number of questions answered correctly by Bob = 8

Probability of Alice answering a question correctly = 0.6

Probability of Alice answering a question incorrectly = 1- 0.6 = 0.4

Probability of Bob answering a question correctly = 0.8

Probability of Bob answering a question incorrectly = 1- 0.8 = 0.2

Probability that there exists at least one question on the test which is answered correctly by Alice but not by Bob = 0.6 *0.2 = 0.12