In colorodos pick 4 lottery game you can pay 1 to select a s

In colorodo\'s pick 4 lottery game, you can pay $1 to select a sequence of 4 digits, such as 2089. If you select the same sequence of 4 digits that were drawn, you win $5,000. Find the expected value of this game. What is your excprected value if, over the years, you played this game 10,000 times?

Solution

total number of 4 digit numbers = 10 *10 * 10 * 10 = 10000

probability of winning = 1/10000

expected value = 5000 * 1/10000 + (-1) * 9999/10000

= -$0.5

expected value of 10000 times

= 10000 * -0.5

= -$5000