The Florida lottery game Lotto is played by choosing six numbers from 1 to 53. If these numbers match the ones drawn by the lottery commission, you win the jackpot. The table below shows the probability of winning a $23,000,000 jackpot, along with the amounts and probabilities of other prizes. Assuming that the jackpot was not split among multiple winners, find the expectation for buying a $1 lottery ticket. Round to the nearest tenth of a cent.

Question

The Florida lottery game Lotto is played by choosing six numbers from 1 to 53. If these numbers match the ones drawn by the lottery commission, you win the jackpot. The table below shows the probability of winning a $23,000,000 jackpot, along with the amounts and probabilities of other prizes. Assuming that the jackpot was not split among multiple winners, find the expectation for buying a $1 lottery ticket. Round to the nearest tenth of a cent.

Match 6 $23,000,000
1
22,957,480
Match 5 $4173
141
11,478,740
Match 4 $56
3243
4,591,496
Match 3 $5
16,215
1,147,874

Answer 1

To calculate the expectation for buying a $1 lottery ticket, we need to multiply the amount of money won for each possible outcome by the probability of that outcome occurring.

For matching 6 numbers and winning the jackpot:
$23,000,000 * (1/22,957,480) = $1.001

For matching 5 numbers:
$4,173 * (141/11,478,740) = $0.057

For matching 4 numbers:
$56 * (3,243/4,591,496) = $0.039

For matching 3 numbers:
$5 * (16,215/1,147,874) = $0.070

The expectation for buying a $1 lottery ticket is the sum of these values:
$1.001 + $0.057 + $0.039 + $0.070 = $1.166

Therefore, the expectation for buying a $1 lottery ticket is approximately $1.17.

Answer 2

To find the expectation for buying a $1 lottery ticket, we need to calculate the expected value for each prize and multiply it by the corresponding probability.

For the jackpot (Match 6), the probability of winning is 1 in 22,957,480, and the prize amount is $23,000,000. The expected value for the jackpot is calculated as follows:

(1/22,957,480) * $23,000,000 = $1

For the Match 5 prize, the probability of winning is 1 in 11,478,740, and the prize amount is $4,173. The expected value for the Match 5 prize is calculated as follows:

(1/11,478,740) * $4,173 = $0.36

For the Match 4 prize, the probability of winning is 1 in 4,591,496, and the prize amount is $56. The expected value for the Match 4 prize is calculated as follows:

(1/4,591,496) * $56 = $0.01

For the Match 3 prize, the probability of winning is 1 in 1,147,874, and the prize amount is $5. The expected value for the Match 3 prize is calculated as follows:

(1/1,147,874) * $5 = $0.004

To calculate the overall expectation, we add up the expected values for all the prizes:

$1 + $0.36 + $0.01 + $0.004 = $1.374

Therefore, the expectation for buying a $1 lottery ticket is $1.374 (rounded to the nearest tenth of a cent).