In the practice problems here, you will be finding probabilities for a random variable. The following table represents the probability distribution for *X,* the employment status of adults in a city.

## Sample questions

If you select one adult at random from this community, what is the probability that the individual is employed part-time?

**Answer:**0.10From the table, you see that 0.10 or 10% of the adults in the city are employed part-time. Using notation, this means that

*P*(*part-time*) = 0.10.If you select one adult at random from this community, what is the probability that the individual isn't retired?

**Answer:**0.82Because total probability is always equal to 1, the probability that someone isn't retired is 1 minus the probability that the person is retired (which, according to the table, is 0.18 in this case). So the probability that the adult isn't retired is 1 – 0.18 = 0.82, or 82%. Using notation, this means that

*P*(*not retired*) = 0.82.If you select one adult at random from this community, what is the probability that the individual is working either part-time or full-time?

**Answer:**0.75Because the categories don't overlap, the probability that someone is working either part-time or full-time is the sum of their individual probabilities. You can see from the table that the probability for part-time employment is 0.10 and for full-time employment, 0.65. Add these two probabilities to get your answer: 0.10 + 0.65 = 0.75, or 75%. Using notation, this means that

*P*(*part-time or full-time*) = 0.75.

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