Question

According to a national marketing survey of American households, 60% of households surveyed had incomes greater than $25,000. The survey also found that 80% of households with income greater than $25,000 in two cars, while households with income less than $25,000 had two cars 40% of the time. What is the probability that household had income greater than $25,000 given that it had two cars? (Round to nearest percentage) A. 42 B. 75 C.25 D. 69 Reset Selection

Answer 1

The correct option is B. 75 [ANSWER]

Explanation:

Let us define the following events:
A: a household has income greater than $25,000

=> A^c: a household has income less than $25,000

B: a household owns two cars

Now, we are given that 60% of the households had incomes greater than $25,000, thus we get:

P(A) = 60% = 0.6

=> P(A^c) = 1 - P(A) = 1 - 0.6 = 0.4

Moreover, we are given that 80% of households with income greater than $25,000 own two cars, thus we get:
P(two cars | income greater than $25,000) = P(B|A) = 80% = 0.8

Moreover, we are given that households with income less than $25,000 has two cars 40% of the time, thus we get:

P(two cars | income less than $25,000) = P(B|A^c) = 40% = 0.4

Now, the probability that a household had income greater than $25,000 given that it has two cars is given by:

P(A)P(BA) P(AB) P(A)P(BA) + P(A) P(BA) [Using Bayes Theorem 0.6 * 0.8 0.6 * 0.8 +0.4 * 0.4 0.48 0.48 + 0.16 0.48 0.64 3 = 4 = 0.75 75% ANSWER

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