# State Lottery and Coin Toss.

Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from 4 hidden windows. Behind each is one of the following: $150,000, $200,000 $1 million, or a "stopper". Before beginning, the contestant is offered $100,000 to stop. Mathematically speaking, should the contestant take the $100,000?

Suppose you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?

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50. If the contestant plays, his expected winnings are given by:

(please see the attached file)

On the other hand, if the contestant stops, he will only win $100,000. Thus it is ...

#### Solution Summary

In this solution, we solve two problems in probability theory involving expected value. Response includes Microsoft Word attachment.