Question

If you bet $1 in Kentucky’s Pick 4 lottery game, you either lose $1 or gain $4,999. (The winning prize is $5,000, but your $1 bet is not returned, so the net gain is $4,999.) The game is played by selecting a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $1 on 1234, what is the expected value of your gain or loss?

Answer 1

The expected value of loss is -$0.5.

Explanation:

Consider the provided information.

We need to select a four digit number between 0000 and 9999.

The two outcomes are either you lose $1 or you gain $4999.

If you bet $1 on 1234, then

The probability of losing is:
`(9999)/(10000)`

The probability of winning is:
`(1)/(10000)`

The expected value of gain or loss is:

`EV=\sum P(x_i)* X_i`

`EV=-1*(9999)/(10000)+4999*(1)/(10000)`

`EV=-0.9999+0.4999`

`EV=-0.5`

Hence, the expected value of loss is -$0.5.