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.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
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
Suppose 28 people arrested for DUI in Illinois are selected at random.
This means that
a) What is the probability that exactly 3 people are repeat offenders
This is
22.60% probability that exactly 3 people are repeat offenders