There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $15

Question

There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $1500, another is worth $1300, and two are worth $1000.

But, wait!!! You are also told that, in the rest of the spaces, there will be a PENALTY of $100 that you have to pay to the host as a penalty for not making the "wise" (winning) choice. You can keep playing until you win ONE of the cash amounts.

Your other choice is a sure prize of $500 cash, IF you just take the money and walk away. Period. No questions asked.....

So, which choice will it be? Take the money and run OR play the odds?

EXPLAIN YOUR CHOICE STATISTICALLY.

(WHAT IS THE MAXIMUM AMOUNT OF THE PENALTY YOU WOULD HAVE TO PAY FOR BAD CHOICES UNTIL YOU WON THE LOWEST AMOUNT? WOULD YOU COME OUT AHEAD?)

Explanation / Answer

I'm assuming you only get ONE pick

If so, the way you calculate the expectation value is to add up all the prizes, times the probability of winning that prize:

E(x) = $1500 * 1/16 + $1300 * 1/16 + $1000 * 2/6 + (-$100) * 12/16
E(x) = $3600 / 16 = $ 225

b) This is NOT a trivial decision. Yes - you have a higher expectation value by walk away and not playing the game,and also there's also a high level of risk - your most likely result is to lose $100. Personally I would take the $500, because if I play the game I just would win $225

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