Question: 172 game show uncertainty in the final round of a...
17-2: Game Show Uncertainty: In the final round of a TV game show, contestants have a chance to increase their current winnings of $1 million to $2 million. If they are wrong, their prize is decreased to $500,000. A contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?
Please double check these calculations and help me to develop the rational for why it is so.
What is known:
Current winnings: 1M
Probability of winning: 0.5; if he wins, he gets: 2M (get 1M).
Probability of losing 0.5; if he loses, he gets: $500, 000 (loses 500,000).
Therefore: 0.50 x $1,000,000 = $500,000 0.50 x $500,000 = $250,000
Since $500,000, (the probability of him winning is greater than) $250,000, he should play.
I need help with the answer below: I'm not sure which equation is bet for this answer. How do I develop the rationale for the right calculation?
If lowest probability =p,
Then the lowest probability that would make it profitable to play is 33%.
OR Equation #2