The prizes and corresponding chances are listed here:

Question

Prize: $50,000, 5,000, 100, 20

Chances: 1 in one million, 1 in 250,000, 1 in 5,000, 1 in 500

 

X stands for your winnings

 

A) list the probability distribution of x. ( Caution what is not listed is the chances of winning nothing).

 

B) calculate your expected winnings.

Answer 1

If we dont care about the cost of the ticket, then all we do is multiply each possible winning by its respective probability and add them up:

 

X              P(X)                X*P(X)
50000       0.000001         0.05000
5000         0.000004         0.02000
100           0.0002             0.02000
20             0.002 0           .04000
0               0.997795         0.00000

                                        SUM 0.13000

So the sum of all the X*P(X) is 0.13 so your expected earnings would be 0.13  (13 cents).  Now realistically if you were to buy the lottery ticket for $1 say, then the expected earnings would be negative, meaning you would lose money and the lottery gains money. The problem is most people don't want to think of all the money they spend on playing the lottery and just remember the payouts.