In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, "Hit the Jackpot," is advertised to have a 1-in-4.37 chance of winning, and a 1-in-664,457 chance of hitting the top prize of $200,000. All of the seven top prizes are still available. If you buy five of these tickets and outcomes are independent, the probability that you win all five times is:
A)6.27%.
B)0.627%.
C)0.0627%.
D)0.0063%.

Question

Quizplus · Accepted Answer

The probability of winning the "Hit the Jackpot" game once is 1/4.37. The probability of winning 5 times in a row is (1/4.37)^5.

The probability of hitting the top prize of $200,000 is 1/664,457. Since all seven top prizes are still available, the probability of hitting one of these prizes on any given ticket is 7/664,457. The probability of hitting a top prize on all five tickets is (7/664,457)^5.

Now we can combine these probabilities using the multiplication rule of probability:
(1/4.37)^5 * (7/664,457)^5 ≈ 0.000627 or 0.0627%.

Therefore, the best choice is C.

In the Virginia Instant Lottery, There Are 10 Different $5