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: 0.10
From 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: 0.82
Because 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: 0.75
Because 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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