According to Discover magazine, 95% of Indy race drivers will survive a crash.
What is the probability that exactly 12 of 15 Indy race drivers survive a crash?

3.07% probability that exactly 12 of 15 Indy race drivers survive a crash

Step-by-step explanation:

For each driver, there are only two possible outcomes. Either they survive a crash, or they do not. The probability of a driver surviving a crash is independent from other drivers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which

And p is the probability of X happening.

95% of Indy race drivers will survive a crash.

This means that

What is the probability that exactly 12 of 15 Indy race drivers survive a crash?

This is P(X = 12) when n = 15. So

3.07% probability that exactly 12 of 15 Indy race drivers survive a crash