In new jersey's pick 4 lottery game, you pay 50 cents to select a sequence of four digits, such as 1332. if you select the same sequence of four digits that are drawn, you win and collect $2788.
1. Find the expected value?
can you select 0 as a lead digit, as in 0345? If so
EV=.50*1/10,000= a tad below nothing.
To find the expected value, we need to calculate the probability of winning and losing and multiply it by the respective amount won or lost.
Step 1: Calculate the probability of winning.
In the Pick 4 lottery, there are 10,000 possible combinations of four digits (from 0000 to 9999). Since we can select any sequence of four digits, the probability of selecting the winning sequence is 1 out of 10,000.
Probability of winning = 1/10,000 = 0.0001
Step 2: Calculate the amount won.
If we win, we collect $2788.
Amount won = $2788
Step 3: Calculate the probability of losing.
To calculate the probability of losing, subtract the probability of winning from 1.
Probability of losing = 1 - 0.0001 = 0.9999
Step 4: Calculate the amount lost.
To play the lottery, we pay 50 cents.
Amount lost = $0.50
Step 5: Calculate the expected value.
The expected value (EV) is calculated by multiplying the probability of winning by the amount won and subtracting the probability of losing multiplied by the amount lost.
EV = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
= (0.0001 * $2788) - (0.9999 * $0.50)
= $0.2788 - $0.4999
= -$0.2211
The expected value of playing the New Jersey's Pick 4 lottery game is -$0.2211. This means, on average, you can expect to lose about 22.11 cents for every 50 cents you spend playing the game.