Question

 

The accompanying data are from an article. Each of 307 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not.

	Hybrid	Not Hybrid
Male	78	116
Female	31	82

Suppose one of these 307 individuals is to be selected at random.

(a)

Find the following probabilities. (Round your answers to three decimal places.)

(i)

P(male)

(ii)

P(hybrid)

(iii)

P(hybrid|male)

(iv)

P(hybrid|female)

(v)

P(female|hybrid)

(b)

For each of the probabilities calculated in part (a), write a sentence interpreting the probability.

(i)

P(male)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.

    The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(ii)

P(hybrid)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.  

  The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(iii)

P(hybrid|male)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.

  The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(iv)

P(hybrid|female)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.

The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(v)

P(female|hybrid)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.  

  The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(c)

Are the probabilities

P(hybrid|male)

and

P(male|hybrid)

equal? If not, explain the difference between these two probabilities.

No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.

No, the probabilities are not equal. The first is the probability that a hybrid Honda Civic owner is male, and the second is the probability that a male Honda Civic owner purchased a hybrid.    

Yes, the probabilities are equal.

Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Let E denote the event that the first airline's flight is fully booked on a particular day, and let F denote the event that the second airline's flight is fully booked on that same day. Suppose that P(E) = 0.7, P(F) = 0.6, and P(E ∩ F) = 0.56.

(a) Calculate P(E | F) the probability that the first airline's flight is fully booked given that the second airline's flight is fully booked. (Round your answer to three decimal places.)


(b) Calculate P(F | E). (Round your answer to three decimal places.)

Answer 1

1)

Suppose one of these 307 individuals is to be selected at random.

	hybrid	not hybrid
male	78	116	194
female	31	82	113
	109	198	307

(a)

Find the following probabilities. (Round your answers to three decimal places.)

(i)

P(male)
= 194/307

(ii)

P(hybrid) = 109/307

(iii)

P(hybrid|male)
=78/194

(iv)

P(hybrid|female)
=31/113

(v)

P(female|hybrid)
=31/109

(b)

For each of the probabilities calculated in part (a), write a sentence interpreting the probability.

(i)

P(male)
C) The probability that a randomly selected Honda Civic owner is male.

(ii)

P(hybrid)

D) The probability that a randomly selected Honda Civic owner purchased a hybrid.

(iii)

P(hybrid|male)

A) The probability that a randomly selected male Honda Civic owner purchased a hybrid.

(iv)

P(hybrid|female)

B)The probability that a randomly selected female Honda Civic owner purchased a hybrid.

(v)

P(female|hybrid)

E) The probability that a randomly selected hybrid Honda Civic owner is female.

(c)

Are the probabilities

P(hybrid|male)

and

P(male|hybrid)

equal? If not, explain the difference between these two probabilities.

A)
No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.