# Expected Value (probability problem)

1. Oct 11, 2009

### snoggerT

Prizes and the chances of winning in a sweepstakes are given in the table below.
Prize: Chances
$25,000,000: 1 chance in 400,000,000$250,000: 1 chance in 150,000,000
$75,000: 1 chance in 50,000,000$10,000: 1 chance in 4,000,000
$800,000: 1 chance in 500,000 A watch valued at$70: 1 chance in 8,000

Find the expected value (in dollars) of the amount won by one entry.

E(X) = X_1*P(X_1)+X_2*P(X_2)+....

3. The attempt at a solution

I used the formula listed above and do not get the right answer. I'm really unsure as to why that doesn't work. I use the dollar values for my X and then the chance as my P(X). Can someone explain to me where my fault is in working this problem?

2. Oct 11, 2009

### Staff: Mentor

Please show us your work. It might be that you made an arithmetic mistake that is causing your answer to be incorrect.

As a side note, it's odd that the probability of winning $25M is relatively high, compared to the probability of winning a prize that is only 1% of that. Also, you show 1 chance in 4 million of winning$10,000, for 1 chance in 1/2 million of winning $800,000. Are you sure that you have written all the prizes and their probabilities exactly as presented in the problem? 3. Oct 11, 2009 ### snoggerT - I copied the values straight from the webwork homework. I do find it very odd that the numbers go from$10,000 @ 1/4,000,000 chance to $800,000 @ 1/500,000 chance. But here is how I worked the problem: E(X) = (25,000,000*(1/400,000,000))+(250,000*(1/150,000,000))+(75,000*(1/50,000,000))+(10,000*(1/4,000,000))+(800,000*(1/500,000))+(70*(1/8,000)) = 1.67691666666667 4. Oct 11, 2009 ### Mark44 ### Staff: Mentor I don't see anything wrong with it. I get the same answer. 5. Oct 11, 2009 ### snoggerT - yeah, I'm at a loss. Maybe the numbers are showing up wrong in relation to the actual answer. 6. Oct 11, 2009 ### snoggerT Alright, I figured it out. The$800,000 value is supposed to be $800. So I suppose my professor made a typo when setting the problem up. 7. Oct 12, 2009 ### Mark44 ### Staff: Mentor If you get the "right" answer when you replace$800K by \$800, that probably is what happened.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook