Probability

A survey of 1,200 men and women asked, "Do you earn over $75,000 per year?" The table below shows the responses for males and females.

Male Female Total
Income over $75,000 585 485 1,070
Income below $75,000 65 65 130
Total 650 550 1200
Based on these data, are "being female" and "earning over $75,000" independent events? (5 points)

No, P(being female | the person earns over $75,000) = P(being female)
No, P(being female | the person earns over $75,000) ≠ P(being female)
Yes, P(being female | the person earns over $75,000) = P(being female)
Yes, P(being female | the person earns o

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  1. P(being female | the person earns over $75,000)
    =P(F∩O)/P(O)
    =(585/1200)/(1070/1200)
    =585/1070

    P(F)=650/1200

    =>P(F∩O)/P(O) ≠ P(F),
    i.e. P(F∩O) ≠ P(F)*P(O)
    therefore they are not independent.

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