Question

Could someone please show me how to do this problem? The instructions say to use Baye’s theorem and make a tree diagram. Thank you!

15) 43% of the workers at Motor works are female, while 64% of the workers at City Bank are female. If 15) one of these companies is selected at random (assume a 50-50 chance for each), and then a worker is selected at random, what is the probability that the worker is female, given that the worker comes from City Bank? A) 43% B) 27.5% C) 21.5% D) 32%

Answer 1

Probability that a worker is female in motor works = .43

and , probability that a worker is female in city bank = .64

Probability of selecting each company is equal = 0.5

Suppose there are 100 employees in each company then we can make the following table:

	male	female	total
city bank	36	64	100
motor works	57	43	100
total	93	107	200

So, P(selected worker is female | she works in city bank ) = 64 / 200 = 0.32

We can see it like

A = city bank and A' = motor works

B = female and B' = male

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

= 0.64 X 0.5

= 0.32