Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the price for the one winning ticket is to be $500. What is your expected value?

(1/1000)*500 + (999/1000)*0. = ?

To calculate the expected value, we need to multiply each possible outcome by its probability of occurring and sum them up. In this case, there are two possible outcomes: winning the lottery (with a $500 prize) and not winning the lottery (with a $0 prize).

The probability of winning the lottery can be determined by dividing the number of favorable outcomes (1) by the total number of possible outcomes (1,000). Therefore, the probability of winning is 1/1,000.

To calculate the expected value, we multiply each outcome by its probability:

(Prize if you win) * (Probability of winning) + (Prize if you don't win) * (Probability of not winning)

Expected Value = ($500 * 1/1,000) + ($0 * 999/1,000)
Expected Value = $500/1,000 + $0
Expected Value = $0.5 + $0
Expected Value = $0.5

Therefore, the expected value of buying one ticket for $1 in this lottery is $0.50.