According to a survey of Australian households,the probability that the residents own two cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had two cars.
-The probability that the residents of a household own two cars and have an income over $50,000 a year is
A) 0.12.
B) 0.18.
C) 0.22.
D) 0.48.

Question

Quizplus · Accepted Answer

Let A be the event that a household has an annual income over $50,000 and B be the event that a household owns two cars. We are given:

P(B | A) = 0.8 (probability of owning two cars if income is over $50,000)
P(A) = 0.6 (probability of income being over $50,000)
P(B) = 0.7 (probability of owning two cars)

We want to find P(A ∩ B), the probability that a household has an income over $50,000 and owns two cars. We can use the formula:

P(A ∩ B) = P(B | A) * P(A)

(which can be derived from the formula for conditional probability)

Substituting the values given,

P(A ∩ B) = 0.8 * 0.6 = 0.48

Therefore, the probability that the residents of a household own two cars and have an income over $50,000 a year is 0.48 or 48%, which corresponds to choice (D).

According to a Survey of Australian Households,the Probability That the Residents