Respuesta :
Answer:
22.60% probability that exactly 3 people are repeat offenders
Step-by-step explanation:
For each driver arrested selected, there are only two possible outcomes. Either they are repeat offenders, or they are not. The probability of an arrested driver being a repeat offender is independent from other arrested drivers. So we use the binomial probability distribution to solve this problem.
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.
In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders;
This means that [tex]p = 0.09[/tex]
Suppose 28 people arrested for DUI in Illinois are selected at random.
This means that [tex]n = 28[/tex]
a) What is the probability that exactly 3 people are repeat offenders
This is [tex]P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{28,3}.(0.91)^{25}.(0.09)^{3} = 0.2260[/tex]
22.60% probability that exactly 3 people are repeat offenders
