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Unemployed Workers: Recent Downtrend in Economy

During a recent downtrend in the economy, 30% of the workforce in a medium sized United States town was unemployed, 20% were eligible for food stamps and 10% fell into both categories. If a worker is selected at random in this town, find the probability that he or she

a. is unemployed and eligible for food stamps.

b. is unemployed or eligible for food stamps.

c. is unemployed but not eligible for food stamps.

d. Are the events "a worker is unemployed" and "a worker is eligible for food stamps" mutually exclusive ? Explain.

e. Find the probability that an unemployed person will be eligible for foodstamps.

f. Find the probability that a person eligible for foodstamps will be employed.

g. Are the events "a worker is unemployed" and "a worker is eligible for foodstamps" independent ? Explain.

Solution Preview

Unemployed: A = 30%
Food stamps: B = 20%
Both: A∩B = 10%

a. is unemployed and eligible for food stamps.
This is the group of A∩B (10%).
So the probability is 0.1

b. is unemployed or eligible for food stamps.
This is the sum of two groups minus the 10% group.
P = (A U B)- (A∩B) = ...

Solution Summary

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