List prob. dist., find expected winnings for sweepstakes

T

trackgirl000

New member
Joined
Jan 30, 2007
Messages
9
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.
 
Here is my take on the outcomes, x, and their probabilities, P(x):

Code: 
+------+----------+----------+--------+-------+----------+
|   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
 
You must log in or register to reply here.
Top