HARD STATS QUESTIOn?

Question

You have just won 64,000 on the TV show "Who wants to be a Millionaire" You can either quit with those winnings or risk answering another question. If you answer correct, then you win 128,000/ If incorrect your winnings fall to 32,000. Using the expected value of winnings, and taking only these three values into account, complete the following sentence.
I should risk answering another question if and only I am at least ___ percent confident of answering it correct.

Answer 1

you gain to win 64,000 dollars if correct, and gain to lose 32,000 dollars if you are wrong. This shows that you win twice as much as you lose. For this reason, in order to take this choice, you should be sure that you get your answer correct at least once out of every 3 tries, because if you win once out of 3 times, you will get back to where you started (lose twice is losing 64,000, and winning once is gaining 64,000 back, so u stay the same). This means you should win 33.333333333% of the time, or 1/3 times. You should risk answering the question if, and only I am at least (33.333333333334) percent confident of answering it correct, because you want to win more than u lost, it should be slightly higher than 33.333333333, so 33.3333333334, or just x>(1/3)

Hope this helps.

Answer 2

33.4%