Question

) A contestant on a quiz show is presented with two questions Q1 and Q2, which she can answer in any order she chooses. Once she chooses which question to try first, she is allowed to go on to the other question only if her answer to the question she chose is correct. The contestant receives $200 for answering Q1 correctly, and $300 for answering Q2 correctly. The probability that she knows the answer to Q1 is 0.7, and the probability that she knows the answer to Q2 is 0.6. In order to maximize her expected winnings, what question should she try first?

Answer 1

There are two scenarios as follows.

Selecting Q1 first-

Suppose, random variable X denotes winning (in dollar) when Q1 is selected first.

So, expected winnings is given by

Selecting Q2 first-

Suppose, random variable Y denotes winning (in dollar) when Q2 is selected first.

So, expected winnings is given by

Hence, in order to maximise her expected winnings, she should try Q1 first.