What is the probability that both man and woman are working?
What will be an ideal response?
P(both man and woman are not working) = 1 - .88 = 0.12
P(woman doesn't work | man doesn't work) = 0.40
P(man does not work) = P(both man and woman are not working) / 0.40
= 0.12 / 0.40 = 0.30
P(man does not work) = P(man doesn't work and woman doesn't work)+
P(man doesn't work and woman works)
Then, 0.30 = 0.12 + P(man doesn't work and woman works)
Hence, P(man doesn't work and woman works) = 0.30 - 0.12 = 0.18
P(woman does work) = P(woman works and man works) +
P(woman works and man does not work)
Then, 0.40 = P(woman works and man works) + 0.18
Hence, P(woman works and man works) = 0.40 - 0.18 = 0.22
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