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?
Well, let's calculate the expected value of playing the New Jersey Pick 4 lottery game. To do this, we need to consider the probability of winning and the prize amount.
The probability of winning is 1 out of 10,000 since there are 10,000 possible combinations of four digits (from 0000 to 9999).
The prize amount is $2788.
So, the expected value can be calculated using the formula:
Expected value = (Probability of winning) * (Prize amount)
Expected value = (1/10,000) * ($2788)
Expected value = $0.2788
So, the expected value of playing the New Jersey Pick 4 lottery game is approximately 28 cents.
To find the expected value, we need to multiply the probability of winning by the amount you win and subtract the cost of playing.
Let's calculate the probability of winning first. In the Pick 4 lottery, there are 10,000 possible four-digit sequences (from 0000 to 9999). Since you select one specific sequence, the probability of winning is 1 out of 10,000.
Next, let's calculate the amount won. If you win, you collect $2788.
Finally, let's calculate the cost of playing. The cost is $0.50 per play.
Now we can calculate the expected value using the formula:
Expected value = (Probability of winning × Amount won) - Cost of playing.
Expected value = (1/10,000) × $2788 - $0.50
Expected value = $0.2788 - $0.50
Expected value = -$0.2212
The expected value of playing the New Jersey's Pick 4 lottery game is -$0.2212. This means that, on average, you would lose $0.2212 for each play.
To find the expected value, we need to calculate the probability of winning and losing, as well as the corresponding payoffs.
First, let's determine the probability of selecting the correct sequence of four digits. In the Pick 4 lottery game, there are ten possible digits (0-9) for each position, and the same digit can be repeated, so there are a total of 10,000 possible outcomes (10^4 = 10,000).
Therefore, the probability of selecting the correct sequence is 1 in 10,000, or 1/10,000.
Next, let's calculate the payoff. If you win, you collect $2,788. However, since the game costs 50 cents to play, we need to subtract that cost from the payoff to get the net winnings. So the net payoff is $2,788 - $0.50 = $2,787.50.
Now we can calculate the expected value. The expected value is the sum of the probabilities of each outcome multiplied by its corresponding payoff.
Expected Value = (Probability of Winning) * (Net Payoff if Win) + (Probability of Losing) * (Net Payoff if Lose)
Expected Value = (1/10,000) * ($2,787.50) + (1 - 1/10,000) * ($0)
Simplifying, we have:
Expected Value = ($2,787.50) + ($0)