Respuesta :
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
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
Based on the data, it is found that "being female" and "earning over $50,000" are not independent events.
What are independent events?
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
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:
[tex]P(A) = \frac{450}{1000} = 0.45[/tex]
850 earn over $50,000, hence:
[tex]P(B) = \frac{850}{1000} = 0.85[/tex]
375 are women who earn over $50,000, hence:
[tex]P(A \cap B) = \frac{375}{1000} = 0.375[/tex]
The multiplication of the probabilities is:
[tex]P(A)P(B) = 0.45(0.85) = 0.3825[/tex]
Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], the events are not independent.
You can learn more about independent events at https://brainly.com/question/14478923
