# Roulette Expected Winnings Discrete Math

Someone is playing Roulette. Here is an example of an outcome: If a player bets on a single outcome the payout is 35 to 1 – meaning if the player guesses the correct answer and puts down a dollar, he/she wins 35 dollars; otherwise, he/she loses a dollar (the dollar used to make the bet).

a.) For a straight bet, 3-number bet and 18-number bet, derive the probabilities for winning and losing and the expected winning amount. That is, explain why the stated values are correct.

b.) If you had only a dollar to spend, which game will you play? Why? Would you do something different if you had twenty dollars to spend?

I'm not sure what it means to derive the probabilities. I have used this equation to solve each of expected outcomes:

(Probability Winning)(Amount Won Per Winning Bet) - (Probability of Losing)(Amount lost per losing bet)

An example of the straight bet was: ($$\frac{1}{38}$$)(35)-($$\frac{37}{38}$$)(1), which would come out to approximately -.052 expected earnings, which is -\$0.05. This is the same for every outcome, so the expected outcomes are the same across the board. So to answer B, I would say that it really doesn't matter which you spend your money on, both dollar and twenty dollars because the expected winnings will be the same. What concerns me about all of this is what A wants me to do...

Should I just list out exactly how I did above with my first example would you think or is there something more?