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 of winning at least once in these five draws is:
A)0.353.
B)0.459.
C)0.727.
D)0.771.

Question

Quizplus · Accepted Answer

The probability of winning at least once in five draws can be found using the complementary probability (probability of not winning in any of the five draws) and then subtracting it from 1.

The probability of not winning in any single draw is 1 - 1/4.37 = 0.77042. Therefore, the probability of not winning in any of the five draws is (0.77042)^5 = 0.1867.

So the probability of winning at least once in five draws is 1 - 0.1867 = 0.8133 which is very close to the Choice C (0.727). Hence, the answer is C.

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