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20 April, 23:47

According to a survey of American households: The probability that a household owns 2 cars, if annual income is over $25,000, is 0.80. Of the households surveyed, 60% had an income over $25,000. Of the households surveyed, 70% had 2 cars. Given your answers to #6 and #7, what is the probability that a household owns 2 cars AND has an income of greater than $25,000 a year

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  1. 21 April, 02:17
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    Answer: 0.48

    Explanation:

    P (A/B) = P (AnB) / P (B) where:

    P (A/B) = The probability of event A occurring given that B has occurred.

    P (AnB) = The probability of both events A and B occurring.

    P (B) = the probability that event B occurs.

    So let

    P (A) = Probability that the residents of a household own 2 cars.

    P (B) = Probability that the annual household income is greater than $25,000.

    The question tells us that

    P (A/B) = 0.8

    Note that: P (A) = 0.7, P (B) = 0.6.

    Since we want to work out P (AnB), because it gives the probability that residents have an annual household income over $25,000 and own 2 cars.

    We would Rearrange our initial equation to make P (AnB) the subject formula becoming;

    P (A/B) = P (AnB) / P (B)

    P (B) * P (A/B) = P (AnB)

    So, inserting our probabilities into this equation gives:

    0.6*0.8 = 0.48
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