Help with Probability Question!!!

Question

Of all the college degrees awarded in the United States, 50% are bachelors degrees, 59% are earned by women, and 29% are bachelors degrees earned by women. Make Venn diagram and use it to answer the question.

What percent of all degrees are earned by men?

What percent of all degrees are bachelors degrees earned by men?

Are the events earning a bachelor's degree and being a man independent? Why?

Answer 1

Venn Diagram:

Create two overlapping circles, one for "Bachelor's Degrees" and the other for "Degrees Earned by Women". The overlapping section represents the intersection: "Bachelor's Degrees Earned by Women".

Populate the Diagram:

1. 1. Total:
2. The entire area of the Venn diagram represents all college degrees awarded in the United States.
3. 2. "Bachelor's Degrees" Circle:
4. The "Bachelor's Degrees" circle should have a total of 50% of the entire area.
5. 3. "Degrees Earned by Women" Circle:
6. The "Degrees Earned by Women" circle should have a total of 59% of the entire area.
7. 4. Overlap:
8. The overlapping section should have 29% of the entire area (Bachelor's degrees earned by women).
9. 5. Remaining Areas:
10. The part of the "Bachelor's Degrees" circle that's not in the overlap represents bachelor's degrees earned by men (50% - 29% = 21%).
11. The part of the "Degrees Earned by Women" circle that's not in the overlap represents degrees earned by women that are not bachelor's degrees (59% - 29% = 30%).
12. The area outside both circles represents degrees that are neither bachelor's degrees nor earned by women (100% - 50% - 59% + 29% = 11%). 
13. 
    

What the Diagram Shows:

1. 29%: of all college degrees are Bachelor's degrees earned by women.
2. 50%: of all college degrees are Bachelor's degrees.
3. 59%: of all college degrees are earned by women.
4. 21%: of all college degrees are Bachelor's degrees earned by men.
5. 30%: of all college degrees are degrees earned by women that are not Bachelor's degrees.
6. 11%: of all college degrees are neither Bachelor's degrees nor earned by women. 
7. 
   

In Summary: The Venn diagram visually breaks down the distribution of college degrees based on their type (Bachelor's) and the gender of the recipient, allowing for a clear understanding of how these categories overlap and where they diverge.