Answer:
a. 0.5 = 50% probability that the driver is selected as a medium-risk driver.
b. 0.3 = 30% probability that he has been classified as high-risk
c. 0.51 = 51% probability that at least one of them has been classified as high-risk.
Step-by-step explanation:
To solve this question, we need to understand conditional probability, for items a and b, and the binomial distribution, for item c.
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
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.
a. If a driver had an accident during the year, find the probability that the driver is selected as a medium-risk driver.
Event A: Had an accident
Event B: Medium-risk driver
Probability of having an accident:
0.01 of 0.6(low risk)
0.05 of 0.3(medium risk)
0.09 of 0.1(high risk)
So
Probability of having an accident and being a medium risk driver:
0.05 of 0.3. So
Desired probability:
0.5 = 50% probability that the driver is selected as a medium-risk driver.
b. If a driver who had an accident during the I-year period is selected, what is the probability that he has been classified as high-risk?
Event A: Had an accident
Event B: High risk driver.
From the previous item, we already know that P(A) = 0.03.
Probability of having an accident and being a high risk driver is 0.09 of 0.1. So
The probability is
0.3 = 30% probability that he has been classified as high-risk
c. If two drivers who had an accident during the I -year period are selected, what is the probability that at least one of them has been classified as high-risk?
0.3 are classified as high risk, which means that
Two accidents mean that
This probability is:
In which
0.51 = 51% probability that at least one of them has been classified as high-risk.