Quant, probability

CFA Level I Quant
#1

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

Plz guide me to understand this question.

#2

None of those answers make sense; probabilities lie between zero and one.

They probably meant 0.28, 0.76, and 0.88, respectively, but it’s an inexcusably sloppy question.

The key to understanding how to answer the question is to determine the number of ways you can succeed; i.e., how many stocks are either value stocks or stocks selected by the previous manager?

Here are some questions to answer along the way:

  1. How many value stocks are there in the portfolio?

  2. How many growth stocks are there in the portfolio?

  3. How many value stocks did the previous manager select?

  4. How many growth stocks did the previous manager select?

Answer those and we’ll continue.

#3
  1. Value stock in portfolio 40% as question stated
  2. Growth Stock in portfolio 60%
  3. Previous manager selected value stock 28%( 0.7*0.4)
  4. Previous manager selected growth stock 48% ( 0.8*0.6)
#4

Not percentages; numbers of stocks.

#5

If u ignore % sign answer remain the same.
Plz guide me

#6

I’m trying to guide you.

If you want to argue, we can stop now. If not, please give the numbers.

#7
  1. Value stock in portfolio 40 as question stated
  2. Growth Stock in portfolio 60
  3. Previous manager selected value stock 28
  4. Previous manager selected growth stock 48
    Ac to my stat I figured this out
#8

What rule will you use to determine the number of stocks that are either value stocks or were selected by the previous manager?

#9

Additional rule