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?

Answer 1

Answer:

No, P(being female | the person earns over $50,000) ≠ P(being female)

Step-by-step explanation:

Step 1: Find the probability of being female and earning over 50,000  then multiply them.

P(being female)= 450/1000=0.45

P(earning over 50,000)=850/1000=0.85

0.45*0.85=0.38

Step 2: find P(being female and earning over $50,000)

450/850=0.52941176=0.53

Step 3:, then P(A ∩ B) = P(A) • P(B). if it is true then its independent

if not then its not independent.

0.53≠0.38

Answer 2

Given:
Do you earn over $50,000 per year?

                                                    Male           Female            Total
Income over 50,000              475                 375                850
Income below 50,000             75                   75                  150
Total                                           550                 450                1,000

Yes, "being female" and "earning over 50,000" are independent events. Independents events are events that happen where the probability of one event happening is not affected by the happening of the other event. 

In this case, regardless if you are male or female, you can earn over 50,000.
Also if you are female, you either earn under or over 50,000