The odds of winning the top prize in Mega Millions are always one in 302,575,350. The odds of winning the top prize in games like Pick 3 are also fixed. The odds of winning the top prize of $500 Pick 3 are one in 1,000. However, the odds are also influenced by the type of game chosen. For example, if you choose an Exact Order play for $1, your chances of winning the $500 top prize are one in 1,000. If you choose a 6-Way Combo play for $6, your chances of winning the $500 top prize are 1 in 166.7. The odds of winning on a single Combo Play ticket are the same as the odds of winning on six separate Exact Order tickets.

• Display a probability table for this distribution
• Convert the odds to probability. *Example is attached
• What is your expected gain or loss from playing?
• If you played 100 times how much would you expect to win or lose?
• Is it binomial? Explain.
• The following attachment is just an example!!!

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