Answer:
There is a 69.8% probability that a subscriber rented a car during the past 12 months for business or personal reasons.
There is a 30.2% probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.
Step-by-step explanation:
We can solve this problem by building the "Venn Diagram" of these probabilities.
I am going to say that A is the probability that a magazine subscriber rented a car for business reasons.
B is the probability that a magazine subscriber rented a car for personal reasons.
C are those who did not rent a car for either of these reasons.
We have that:
In which a are those who only rented for business reasons and are those who rented both for business and personal reasons.
By the same logic, we have that
In which b are those who only rented for personal reasons.
The sum of the probabilities is 1, so:
We start finding the values from the intersection of these sets.
30% rented a car during the past 12 months for both business and personal reasons. So .
45.8% rented a car during the past 12 months for business reasons
This means that .
And
54% rented a car during the past 12 months for personal reasons
This means that .
And
What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons?
That is the probability that someone rented a car for only one of these reasons, or both. So:
There is a 69.8% probability that a subscriber rented a car during the past 12 months for business or personal reasons.
What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?
This is the value of C
We have that:
[tex]C = 0.302[tex]
There is a 30.2% probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.