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21 July, 16:24

A survey of couples in a city found the following probabilities:

The probability that the husband is employed is 0.85.

The probability that the wife is employed is 0.59.

The probability that both are employed is 0.50.

A couple is selected at random. Find the probability of the following.

(a) At least one of them is employed.

(b) Neither is employed.

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  1. 21 July, 18:39
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    Answer

    (a) 0.94

    (b) 0.06

    Step-by-step explanation:

    P (husband is employed) = P (H) = 0.85

    P (wife is employed) = P (W) = 0.59

    P (both are employed) = P (H∩W) = 0.50

    (a) At least one of them is employed

    = P (H∪W)

    = P (H) + P (W) - P (H∩W)

    =0.85 + 0.59 - 0.50

    =0.94

    (b) Neither is employed,

    =1 - P (H∪W)

    = 1-0.94

    =0.06
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