Consider the following simplified scario based on who wants

Consider the following simplified scario based on who wants to be a millionaire? a game show in which the contestant answeres multiple choice questions that have 4 choices per question. The contestant (fred) has answered 9 questions correctly already, and is now being shown the 10th question. He has no idea what the right answeres are to the 10th or 11th questions are. He has one lifeline available, which he can apply on any question, and which narrows the number of choices from 4 down to 2. Fred has the following options available:

a.) walk ways with 16,000

b.) apply his lifeline to the 10th question, and then answer it. If he gets it wrong, he will leave with 1,000. If he gets it right he moves on to 11th quesion. He then leaves with 32,000 if he gets the 11th question wrong, and 64000 if he gets the 11th question right

c.) same as the previous option, except not using his lifeline on the 10th question, and instead applying it to the 11th question (if he gets the 10th question right)

Solution

The question doesnot state what is required from the given data. I will assume it requires best alternative for fred to choose. If it is otherwise please comment.

Expected return in Option A = $16,000

Expected return in option B = (1/2)1,000+(1/2)(3/4)32,000+(1/2)(1/4)64,000 = $20,500

Expected return in Option C = (3/4)(1,000)+(1/4)(1/2)(32,000)+(1/4)(1/2)64,000 = $12,750

Since in option B the expected amount of return is maximum, that is what fred should choose.