SOLUTION: A survey of couples in a city found the following probabilities: The probability that the husband is employed is 0.82. The probability that the wife is employed is 0.59. The pro

Question 1192877: A survey of couples in a city found the following probabilities:
The probability that the husband is employed is 0.82.
The probability that the wife is employed is 0.59.
The probability that both are employed is 0.52.
A couple is selected at random. Find the probability of the following. (Round your answers to two decimal places.)
(a) At least one of them is employed.

(b) Neither is employed.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

H = husband is employed
W = wife is employed

P(H) = probability husband is employed
P(H) = 0.82 is given

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

P(H and W) = probability husband and wife are employed
P(H and W) = 0.52 is given

P(H or W) = probability husband or wife or both are employed
P(H or W) = probability at least one of them are employed
P(H or W) = P(H) + P(W) - P(H and W)
P(H or W) = 0.82 + 0.59 - 0.52
P(H or W) = 0.89

P(neither are employed) = 1 - P(H or W)
P(neither are employed) = 1 - 0.89
P(neither are employed) = 0.11

Summary:
(a) 0.89
(b) 0.11

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