Question

During playing the game who wants to be a millionaire, Amanda has won $64,000 and is thinking about going for the next question. This means if she gets the next question correct she will go home with $125,000. But if she answers wrong she will only get $32,000. She can choose to walk out now with her $64,000.

What should she do?
Suppose Amanda decides to answer the question. What is the expected value of the outcome?

Answer 1

it is given that if she is right on next question, then she can take $125,000, but if she is wrong, then she can take only $32,000

There are four possible outcomes, suppose she decided to play, then there is 1/2-1/2 probability of winning and losing and there is also 1/2-1/2 probability of whether she will play or leave with $64,000

So, probability of winning $125,000 is only 1/4 [decided to play(1/2 probability) and then wins(1/2) probability, so total 1/2*1/2]

probability of winning $32,000 = 1 - P(winning $125,000) = 1-1/4 = 3/4

So, expected value =

= (1/4*125000)+(3/4*32000)

=31250 + 24000

= $55,250

Expected amount is $55,250