Asurvey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. what is the 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?

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.

it is probably the graph on the bottom right.