2.6 Expected Value

1) A game is played where you roll one standard 6-sided die. To play you must pay $3. If you roll a 1 or 4 you win $5 and if you roll a 2 or 6 you win $1, 3 or 5 wins nothing.

What is the expected value of this game?

2) The game of roulette has 38 outcomes

(1 - 36; 0; 00). A bet on a set of 5 numbers has payoff odds of 6:1. (Win $6 on every dollar bet if you win or you lose $1 if you lose). What is the expected value of this bet?

3) A car insurance company predicts the following payouts. Find the expected payout.

x 0 1,000 2,000 3,000 4,000 5,000 P(x) 0.65 0.10 0.15 0.07 0.03 0.01

4) You are offered a job with 2 pay options. You can get a fixed $400 a week or $200 a week with weekly bonuses given by the following table:

Bonus 0 100 200 300 400 500 P(Bonus) 0.15 0.20 0.12 0.25 0.20 0.08

Which pay option has the higher expected weekly pay? Explain your answer.