Question

Say you're getting lottery tickets. Each one costs $75. There's a 30 percent chance you get one of the low many prizes. The low-level prizes range from 1-5 dollars. There's a 0.5 percent chance of getting a mid-level prize which ranges from 50-125 dollars, and finally, there's the grand prize which is 100,000,000 dollars and there's a 0.002 percent chance of getting it. For every 5 times you get a low-level prize, the chance of mid and grand prizes increase by 0.1 after 2 tries it returns to the normal amount. After ten attempts you automatically get a mid-level prize. So the question is if you know the statistics how many dollars do you have to spend to get the grand prize?

A) Calculate the expected value and compare it with the cost of lottery tickets.
B) $15,000,000
C) $30,000,000
D) It cannot be determined without knowing the number of low-level prizes won.

Answer 1

The expected value is $103.4375, which means on average, you would expect to lose money by playing the lottery. Therefore, option D is the correct answer.

Step-by-step explanation:

To calculate the expected value, we need to find the weighted sum of all possible outcomes. The probability of getting a low-level prize is 30%, so the expected value for a low-level prize is $1.5 (average of 1 and 5 dollars). The probability of getting a mid-level prize is 0.5%, so the expected value for a mid-level prize is $87.5 (average of 50 and 125 dollars). The probability of getting the grand prize is 0.002%, so the expected value for the grand prize is $2,000,000 (100 million dollars). Now we can calculate the expected value by multiplying the probabilities with their respective expected values and summing them up: 0.3 * 1.5 + 0.005 * 87.5 + 0.00002 * 2000000 = $63 + $0.4375 + $40 = $103.4375.

Comparing the expected value of $103.4375 with the cost of each lottery ticket, which is $75, we can see that on average, you would expect to lose money by playing this lottery. Therefore, option D, 'It cannot be determined without knowing the number of low-level prizes won,' is the correct answer.