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# Probability and Game Show

Discrete Probability Distribution ???

Imagine you are in a game show, where there are big money prizes that can be won.

Now, let us start the money give-away! There are 4 prizes hidden on a game board with 16 spaces. One prize is worth \$4000, another is worth \$1500, and two are worth \$1000.

But, wait!!! You are also told that, in the rest of the spaces, there will be a bill of \$50 that you have to pay to the host as a penalty for not making the "wise" choice.

In this modern game show, you are actually given a choice: a real choice.

Choice #1: You are offered a sure prize of \$400 cash, and you just take the money and walk away. Period. No question asked.....

Choice #2: Take your chance and play the game.......
What would be your choice? Take the money and run, or play the game? Why? Please provide an explanation for your choice.

#### Solution Preview

This is an expected value problem. In the first scenario, you could win \$4000, you could win \$1500, you could win \$1000, or you could lose \$50. The issue is how much you are "expected" to win. According to the problem, the probability of winning \$4000 is 1/16; ...

#### Solution Summary

In this problem, I provide an explanation from a statistical point of view for which choice to make in a game show scenario.

\$2.19