Answer:
the expected value of your gain or loss is a net loss of $0.5006.
The probability of winning is 1/10,000 = 0.0001.
Explanation:
There are 10,000 possible four-digit numbers between 0000 and 9999. Only one of those numbers is the winning number. Therefore, the probability of winning the Pick 4 game is:
Probability of winning = 1/10,000 = 0.0001
If you bet $5 on 1234, there are two possible outcomes:
-You lose $5 with probability 0.9999
-You gain $9,995 with probability 0.0001
The expected value of your gain or loss is the sum of the products of each outcome and its probability:
Expected value = (-$5 x 0.9999) + ($9,995 x 0.0001)
Expected value = -$0.5006