Respuesta :
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]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)!}[/tex]
And p is the probability of X happening.
95% of Indy race drivers will survive a crash.
This means that [tex]p = 0.95[/tex]
What is the probability that exactly 12 of 15 Indy race drivers survive a crash?
This is P(X = 12) when n = 15. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{15,12}.(0.95)^{12}.(0.05)^{3} = 0.0307[/tex]
3.07% probability that exactly 12 of 15 Indy race drivers survive a crash
