A contest entrant has a .00001 probability of winning $5,000.00. If this is only prize and the entry fee is $20.00, then what is the expected value?

Regardless of what you pay for an entry "ticket" its expected value is in this case
(probability of winning) x (prize money) = 10^-5 x $5,000 = $0.50

Not a very good bet, if you pay $20 for it

To calculate the expected value, you need to multiply the probability of winning by the prize money. In this case, the probability of winning is 0.00001 (which is equivalent to 10^-5), and the prize money is $5,000.

Expected value = probability of winning x prize money
Expected value = 0.00001 x $5,000
Expected value = $0.05

So the expected value is $0.05. This means that on average, for each entry, you can expect to win $0.05. Since the entry fee is $20, it is not a good bet because the expected value is less than the entry fee.