Google Virginia's Powerball and calculate the probability of winning the jackpot. Use simple conversion if odds instead of probability is reported. Share a link that takes us to the odds information on Virginia's Powerball.

• Set up a probability table for this distribution. For example:

X	P(x)
-$1	.9(lose)
$2	.1(win)

• What is the expected gain or loss from playing?
• If played 100 times how much would you expect to win or lose?

Is it binomial? Explain.

Convert the odds to a probability To convert from odds to a probability, divide the odds by one plus the odds. So, to convert odds of 1/9 to a probability, divide 1/9 by 10/9 to obtain the probability of 0.10. Example: Taking the odds of 1:9 and knowing I'll win 1/10 times I have a probability of .10 of winning. This means I have a probability of .90 (the complement) of losing. Let's say if I spend a dollar, I could possibly win 2 dollars. If I lose, I lose the dollar. My distribution looks like this. X P(X) -$1 .9 (lose) $2 .1 (Win) Calculate expected value: E(x) = Sum (x* P(x)) E(x) = -l(.9) + 2(.l) = -.7 I expect to lose 70 cents ON AVERAGE each time I play. If I play 100 times, I'll lose .7(100) -- expected loss in one game times the number of times I play I expect to lose $70 dollars if I play 100 times. Why do I not expect to lose 100 dollars