Question

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?
yes, these two events are most likely independent, so the joint probability can be found by multiplying the individual probabilities.
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.
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.
yes, the joint probability can always be found by multiplying the individual probabilities.

Explanation:

To find the joint probability of two events \(A\) (owning a house) and \(B\) (having full - time employment), the formula \(P(A\cap B)=P(A)\times P(B)\) holds only if \(A\) and \(B\) are independent events. In real - world scenarios, owning a house (\(A\)) and having full - time employment (\(B\)) are likely not independent. For example, having a full - time job may influence the ability to afford a house (and vice - versa). So, we cannot simply multiply the individual probabilities \(P(A) = 0.6\) and \(P(B)=0.8\) to get \(P(A\cap B)\).

Answer:

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.