Question

Please Help!
In a corporation, 63% of the employees are female, executives, or both. Furthermore, 54% of the employees are female, and 4% are female executives. Find the percentage of employees who are male executives.

Answer 1

Let \(M\) denote male, \(F\) female, \(E\) executive and \(\overline{E}\) not executive.
\[P(F\cup E)=0.63\\
P(F)=0.54\\
P(F\cap E)=0.04\]
Using this info, you're asked to find \(P(M\cap E)\). Does the notation make sense?

Answer 2

Alright, I understand that I have to find the intersection ,but would it be subtracting the union of the female with the intersection of the female? .63-.04?

Answer 3

Not quite. There's a useful formula you'll be using:
\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]
Think of a Venn diagram. If you want to count everything in both \(A\) and \(B\), then you don't want to double-count any items in the sets. This is why we subtract \(P(A\cap B)\).

So, the first thing to do, I think, would be to find \(P(E)\) using this formula.

Answer 4

Oh wait is it subtracting .63-.54?

Answer 5

I got it ! Thank You =)

Answer 6

\[P(F\cup E)=P(F)+P(E)-P(F\cap E)\\
0.63=0.54+P(E)-0.04\\
P(E)=0.13\]

Answer 7

Alright I took note of this for the next problem in my h.w
Thank You I truly appreciate it. I struggle a lot with probability.