Mathematics, 08.10.2019 04:10 fredo99

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?

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Answer from: RobbyO

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:

$A = a + (A \cap B)$

In which a are those who only rented for business reasons and $A \cap B$ are those who rented both for business and personal reasons.

By the same logic, we have that

$B = b + (A \cap B)$

In which b are those who only rented for personal reasons.

The sum of the probabilities is 1, so:

$a + b + (A \cap B) + C = 1$

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 $A \cap B = 0.3$ .

45.8% rented a car during the past 12 months for business reasons

This means that A = 0.458 .

And

$A = a + (A \cap B)$

0.458 = a + 0.3

a = 0.158

54% rented a car during the past 12 months for personal reasons

$B = b + (A \cap B)$

This means that B = 0.54 .

And

$B = b + (A \cap B)$

0.54 = b + 0.3

b = 0.24

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:

$P = a + b + (A \cap B) = 0.158 + 0.24 + 0.30 = 0.698$

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:

$a + b + (A \cap B) + C = 1$

0.698 + C = 1

[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.

Answer from: Quest

; )

step-by-step explanation: ; )

Answer from: Quest

goog may be able to you find that answer

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