Answered

A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% renteda 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 (or both)? What is the probability that s subscriber did not rent a car during the past 12 months for either business or personal reasons?

Answer :

Mistadijex

Answer:

a.) 69.8%

b.) 30.2%

Step-by-step explanation:

For business reasons, 45.8% rented a car P(B) = 0.458

For personal reasons, 54% rented a car P(R) = 0.54

For both business and personal reasons, 30% rented a car = 0.30

Addition rule for two probability events Is denoted as P(X or Y) = P(X) +P(Y) - P(XnY)

a.) Probability that a car was rented for business or personal reason or both = P(B) + P(R) - P(BnR)

= 0.458 + 0.54 - 0.3 = 0.698 = 69.8% probability of renting a car in the past 12 months for business or personal reason(or both).

b.) Probability that a car was NOT rented for business or personal reason = 1 - (Probability that a car was rented for business or personal reason)

= 1 - 0.698 = 0.302 = 30.2% probability of NOT renting a car in the past 12 months.

Answer:

(a) 0.698

(b) 0.302

Step-by-step explanation:

We are given that a survey 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.

Let Probability that magazine subscribers rented a car during the past 12 months for business reasons = P(BR) = 0.458

Probability that magazine subscribers rented a car during the past 12 months for personal reasons = P(PR) = 0.54

Probability that magazine subscribers rented a car during the past 12 months for both business and personal reasons = [tex]P(BR \bigcap PR)[/tex] = 0.30

(a) Probability that a subscriber rented a car during the past 12 months for business or personal reasons is given by = [tex]P(BR \bigcup PR)[/tex]

As we know that;

                      [tex]P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)[/tex]

So, according to our question;

                      [tex]P(BR \bigcup PR) = P(BR) + P(PR) - P(BR \bigcap PR)[/tex]

                                            = 0.458 + 0.54 - 0.30

                                            = 0.998 - 0.30 = 0.698

Hence, probability that a subscriber rented a car during the past 12 months for business or personal reasons (or both) is 0.698.

(b) Probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons = 1 - Probability that a subscriber rented a car during the past 12 months for business or personal reasons

             = 1 - [tex]P(BR \bigcup PR)[/tex]

             = 1 - 0.698 = 0.302

Hence, probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons is 0.302.

Other Questions