Question

A survey of 1,000 men and women asked, "Do you earn over $50,000 per year?" The table below shows the responses for males and females:
Male Female Total
Income over $50,000 475 375 850
Income below $50,000 75 75 150
Total 550 450 1,000


Based on these data, are "being female" and "earning over $50,000" independent events?
Yes, P(being female | the person earns over $50,000) = P(being female)
Yes, P(being female | the person earns over $50,000) ≠ P(being female)
No, P(being female | the person earns over $50,000) = P(being female)
No, P(being female | the person earns over $50,000) ≠ P(being female)

Answer 1

Based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.

What is probability?

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Two events, A and B are independent, if:

P(A $\cap$ B) = P(A) P(B)

In this problem, the events are:

• Event A: Being female.
• Event B: Earning over $50,000.

Out of the 1000 people, 450 are female, hence:

P(A) = $\dfrac{450}{1000}$ = 0.45

850 earn over $50,000, hence:

P(B) = $\dfrac{850}{1000}$ = 0.85

375 are women who earn over $50,000, hence:

P(A $\cap$ B)  = $\dfrac{375}{1000}$ = 0.375

The multiplication of the probabilities is:

P(A $\cap$ B)  = 0.45(0.85} = 0.3825

Therefore based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.

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