In an instant lottery, your chance of winning is 10.0%.If you play the lottery 100 times and the outcomes are independent, the probability that you win at least 15.0% of the time is ______.
A)0.4933
B)0.5
C).15
D)0.0478
E)0.9213

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution.

Let X denote the number of times you win in 100 plays of the lottery. Then X has a binomial distribution with n = 100 and p = 0.1.

To find the probability that you win at least 15% of the time, we need to calculate:

P(X >= 15)
= 1 - P(X < 15)
= 1 - P(X <= 14)
= 1 - binomdist(14, 100, 0.1, true)
≈ 0.0478

Using a calculator or statistical software, we can find that the probability is approximately 0.0478.

Therefore, the best choice is (D).

In an Instant Lottery, Your Chance of Winning Is 10