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.
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
1 answer
1 answer