CFA CFA Level 1 Quant, probability

# Quant, probability

Topic Resolution: Not Resolved
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Alex is examining a portfolio that contains 100 stocks that are either value or Growth. Out of these 100 stocks 40% are value stock. The previous portfolio manager had selected 70% of the value stocks and 80% of the growth stocks. What is the probability of selecting a stock at random that is either a value stock or was selected by previous portfolio manager?

A) 28%
B) 76%
C) 88%

can anyone help me to understand this?

• 2

Probability of selecting a stock at random that is either a value stock or was selected by previous portfolio manager

= Pvalue + Pgrowth by previous PM

= 0.4 + (1-0.4) * (0.8)

= 0.4 + 0.48

= 88% • 0

Hi Zee,

Why is it assumed that the stock selected by the previous portfolio manager must be a growth stock?

Shouldn’t it be a combination of Pgrowth by previous PM + Pvalue by previous PM?

So would be Pvalue + (Pgrowth by previous PM + Pvalue by previous PM) – Intersection of the two (being value stock?)

0.4 + [(1-0.4) * 0.8  + (0.6) * 0.7] – (0.7*0.6)   = 0.88? (Same answer but diff. logic)

• 1

Because if the selected stock was a value stock, that scenario is already covered by my first parameter (Pvalue). If I included it again I would be double counting. Hope that helps! 