Probability question

CFA Level I Quant
#1

Can you help me understand how to solve this question.

In a given portfolio, half of the stocks have a beta greater than one. Of those with a beta greater than one, a third are in a computer-related business. What is the probability of a randomly drawn stock from the portfolio having both a beta greater than one and being in a computer-related business?

Answer is 0.167.

#2

Let:

  • X = the stock has a beta greater than one
  • Y = the stock is in a computer-related business

We’re looking for P(XY). We’re given that:

  • P(X) = 1/2
  • P(Y|X) = 1/3

P(XY) = P(YX)

= P(Y|X)P(X)

=(1/3)(1/2)

= 1/6

#3

Thank you.

#4

Thank you.

#5

You’re welcome.

#6

A simple example: perfect!