Choose an employee person at random. Let A be the event that the person is a female and B be the event that the person holds a managerial position. Data from the US department of labor suggests that P (A) = 0.47 and P (B|A) = 0.34

A) explain what P (A) = 0.47 means in context

B) explain what P (B|A) = 0.34 means in context

C) what is the probability that a randomly chosen employed person is a male?

D) what is the probability that a randomly chosen employed person is a female manager?

E) what is the probability that a randomly chosen employed female is not a manager?

A: Female B: Managerial Position

P (A) = 0.47

P (B|A) = 0.34

Find P (A') - > [Probability that the person is male]

By the complement rule

P (A') = 1 - P (A)

= 1 - 0.47

= 0.53

P (A') = 0.53

So the probability of a male being chosen is 0.53.

2.) P (B|A) = P (B and A) / P (A)

Use the values given P (A) and P (B|A) to find P (B and A) which will be your answer

3.) What is the probability that a randomly chosen employed female is not a manager?

What is the probability that a female is not a manager

Find P (A and B')

Step #1, First Find P (B' | A).

It can be shown that

P (B | A) + P (B' | A) = 1 [ You can verify this with a Venn diagram]

So

0.34 + P (B' | A) = 1

so

P (B' | A) = 0.66

P (B' | A) = P (B' and A) / P (A)

0.66 = P (B' and A) / 0.47

So P (B' and A) = 0.3102

So the chance you will be someone that is female and not a manager is 0.3102.

Hello there.

E) what is the probability that a randomly chosen employed female is not a manager?

0.3102.