In a certain city, 60% of the heads of household own the house in which they reside, and 80% of the heads of the household have full-time employment. When considering what percentage of heads of household both own their home and have a full-time job, a student estimates that 48% of heads of household fit both requirements, stating that (0.60)(0.80) = 0.48. Is this student correct in his approach?
Answer
A
Yes, these two events are most likely independent, so the joint probability can be found by multiplying the individual probabilities.
B
No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent.
C
No, these two events are most likely not independent, so the joint probability cannot be found by multiplying the individual probabilities. They should be added instead.
D
Yes, the joint probability can always be found by multiplying the individual probabilities.
Explanation
Multiplying 0.60 by 0.80 gives the probability that both events occur only if home ownership and full-time employment are independent. These events are likely related, so the given percentages alone do not establish that the joint probability is 48%; you would need more information, such as the percentage of homeowners who work full-time. Choice B correctly identifies the independence issue. Adding the percentages, as choice C suggests, would not give the probability of both events.
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