List prob. dist., find expected winnings for sweepstakes

[trackgirl000]

1. A book club announces a sweepstakes to attract new subscribers. The prizes are the corresponding chances are listed here:
prize chance
$50,000 1 in one million
$5,000 1 in 250,000
$100 1 in 5,000
$20 1 in 500
Suppose you have just mailed in a sweepstakes ticket and X stands for your winnings.
(a) list the probability distribution of X. (caution:what is not listed is the chance of winning nothing, but you can figure that out from the given information).
(b) calculate your expected winnings.

 

[Pilly151]

Here is my take on the outcomes, x, and their probabilities, P(x):

+------+----------+----------+--------+-------+----------+
|   x  |   50000  |   5000   |   100  |   20  |     0    |
+------+----------+----------+--------+-------+----------+
| P(x) | 0.000001 | 0.000004 | 0.0002 | 0.002 | 0.997795 |
+------+----------+----------+--------+-------+----------+

Then the expected value E(x) is given by:

E(x) = 50000(0.000001) + 5000(0.000004) + 100(0.0002) + 20(0.002) + 0 = $0.13