In an instant lottery, your chance of winning is 0.1.If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is closest to __________.
A)0.4933
B)0.5
C).15
D)0.0478
E)0.9213

Question

Quizplus · Accepted Answer

This problem can be approached using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. However, calculating the probability of winning exactly k times for k = 15, 16, ..., 100 directly would be cumbersome. Instead, we can use the normal approximation to the binomial distribution for large n, or recognize that the question asks for the probability of an event that is unlikely to happen given the parameters (winning rate of 0.1, but asking for at least a 0.15 win rate over 100 trials). Without doing the exact calculations, we can infer that the probability of winning at least 15 times out of 100, given a win probability of 0.1, is relatively low. Among the provided options, 0.0478 is the one that best fits this description, indicating a low probability event.

In an Instant Lottery, Your Chance of Winning Is 0