# Homework Help: Intersection of probabilities.

1. Oct 22, 2009

### tjera

Hello,

I need help with this problem:

A: 67,000 Purchasing managers that are male
B: 33,000 purchasing managers that are female
C: 245,000 financial managers that are male
D: 150,000 financial managers that are female
Out of these 495.000 individuals , what is the probability that a randomly selected individual is either a purchasing manager or male?

Isn't this:
P(A or B)-P(B or D)?

Books says =0.697.

2. Oct 22, 2009

### sylas

No. How did you get that?

It's probability purchasing manager or male. Which groups are purchasing manager or male?

3. Oct 22, 2009

### tjera

-How did you get that?
I just thought that might be correct. Purchasing managers, minus, females from purch. managers and financial managers should give the right answer i thought...(i am still not getting these intersection and unions of probability...to confusing).
I also assigned those A,B,C and D, myself t to those categories.
- Which groups are purchasing manager or male?
A is both male and purch. manager, so that would be 0.67, but the book says 0.697.

*confused*

4. Oct 22, 2009

### honestrosewater

There are at least two ways to do this. First, you could save yourself some calculations by noticing that the only outcome that is not included in your event is D: financial managers that are female. All of the other outcomes include either a purchasing manager or a male. So P(purchasing manager or male) = 1 - P(financial manager that is female). What is P(financial manager that is female)?

Yes, but you need "either or", not "and". The people in B are also purchasing managers, and the people in C are also male. So do you not also need to include these?

5. Oct 22, 2009

### tjera

P(financial manager that is female)= P(D)=150

So...what is the definitive way to solve this?

6. Oct 22, 2009

### HallsofIvy

There are 495000 individuals, any of whom is equally likely to be chosen. There are a total of 67000+ 33000= 100000 purchasing managers. There are another 245000 who are male. There are a total of 345000 individuals who are either purchasing managers or male. The probability is 345000/495000= 0.6969696969696969696969696969697

That is P(A or B or C). "PA or B) - P(B or D)" would be the number of people who are purchasing managers minus the number of people who are financial managers- which has nothing to do with this question. Now that I look at it more carefully, I see that P(A or B or C) could be calculated more simply as 1- P(D)= 1- 150000/495000= 0.6969696969696969696969696969697 also. Individuals who are "purchasing managers or male" are simply individuals who are "not both purchasing managers and female".

7. Oct 22, 2009

### tjera

Thank you so much HallsofIvy, that made it very clear! :D