A Financial Consultant has classified her clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gender Bonds Stocks Balanced Male 0.12 0.10 0.15 Female 0.18 0.20 0.25 One client is selected at random, and two events A and S are defined as follows: A: The client selected is male. S: The client selected has a stocks portfolio. Find the probability that the client selected is female, given that the client has a stocks portfolio (i.e. find P(AC IS).

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QUESTION 9
A Financial Consultant has classified her clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily
stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:
Portfolio Composition
Gender
Bonds
Stocks
Balanced
Male
0.12
0.10
0.15
Female
0.18
0.20
0.25
One client is selected at random, and two events A and S are defined as follows:
A: The client selected is male.
S: The client selected has a stocks portfolio.
Find the probability that the client selected is female, given that the client has a stocks portfolio (i.e. find P(AC |S).
O P(AC |S) = 0.10/0.30
O P(AC |S) = 0.30/0.20
O P(AC |S) = 0.25/0.40
O P(AC IS) = 0.20/0.30
Transcribed Image Text:QUESTION 9 A Financial Consultant has classified her clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gender Bonds Stocks Balanced Male 0.12 0.10 0.15 Female 0.18 0.20 0.25 One client is selected at random, and two events A and S are defined as follows: A: The client selected is male. S: The client selected has a stocks portfolio. Find the probability that the client selected is female, given that the client has a stocks portfolio (i.e. find P(AC |S). O P(AC |S) = 0.10/0.30 O P(AC |S) = 0.30/0.20 O P(AC |S) = 0.25/0.40 O P(AC IS) = 0.20/0.30
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