Question

According to Discover magazine, 95% of Indy race drivers will survive a crash.

Answer 1

Answer:

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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}[\tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.[tex]C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

95% of Indy race drivers will survive a crash.

This means that $p = 0.95$

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

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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 12) = C_{15,12}.(0.95)^{12}.(0.05)^{3} = 0.0307$

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