Question

The Knightrola lottery has been updated to allow choosing 6 numbers out of 63 on a $1 ticket.

a. choosing 3 numbers correctly gives a $10 prize.
b. choosing 4 numbers correctly gives a $50 prize.
c. choosing 5 numbers correctly gives a $5,000 prize.

if the lottery expects to precisely break even, how much is its prize for getting all 6 numbers correct?

Answer 1

The prize for getting all 6 numbers correct in the Knightrola lottery is $0.

Step-by-step explanation:

To calculate the expected prize for getting all 6 numbers correct in the Knightrola lottery, we need to determine the probability of getting 6 numbers correct and multiply it by the prize amount. Here are the steps:

1. Calculate the probability of choosing 6 numbers correctly: The probability of choosing a correct number out of 63 is 1/63. Since there are 6 numbers to choose correctly, the probability is (1/63)^6.
2. Multiply the probability by the prize amount: The prize for getting 6 numbers correct is the amount we are trying to find. Let's call it x. So, we have the equation (1/63)^6 * x = 0. This is because the lottery expects to break even, so the total cost of all the tickets sold should equal the total amount of prizes awarded.
3. Solve for x: To solve the equation, we can multiply both sides by (63^6) to get rid of the fraction. This gives us x = 0.

Therefore, the prize for getting all 6 numbers correct in the Knightrola lottery is $0.