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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.