According to the U.S. Census Bureau, 27.3% of U.S. adult women have never married (single), 49.8% of U.S. adult women are married, and 22.8% of U.S. adult women are widowed, divorced, or separated (other). Of the single women, 6.7% are unemployed; of the married women, 2.6% are unemployed; of the “other” women, 4.9% are unemployed. Suppose that a randomly selected U.S. adult woman is found to be unemployed. What is the probability that she is single?

Approach Define the following events:

U: unemployed 

S: single M: married 

O: other 

We have the following probabilities:

and we know that P(U) = 0.042.
We wish to determine the probability that a woman is single, given the knowledge that she is unemployed. That is, we wish to determine P(S|U). We will use Bayes’s Rule as follows:

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P(S) = 0.273 = P(M) = 0.498 P(U|O) P(O) = 0.228 = 0.049 P(US) 0.067 P(U|M) = 0.026