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**CFA Practice Question**

A portfolio manager has identified two sectors for investing. There are a total of 60 securities that belong to these two sectors. Of the sixty securities, 20 belong to sector A and the remaining belong to sector B. Of the sector A securities, 5 are high risk and of the sector B securities, 20 are high risk. If a security is picked randomly, what is the probability that the security belongs to sector A or is a high risk security?

A. 5/12

B. 2/3

C. 3/4

**Explanation:**Prob(High risk or Sector A) = Prob(High risk) + Prob (Sector A) - Prob(High risk & Sector A)

Joint probability, Prob(High risk & Sector A) = Prob(High risk|Sector A) x Prob (Sector A) = (5/20) x (20/60) = 5/60.Thus, Prob(High risk or Sector A) = (25/60) + (20/60) - (5/60) = 40/60 = 2/3.

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**User Contributed Comments**
3

User |
Comment |
---|---|

mary11 |
I don't think I will ever get these prob questions. |

Knapp |
I went crazy using formulas until I realized there's simple logic- there are 20 securities in sector A and 20 (different) high risk securities in sector B. So 20+20/60=2/3. |

cfastudypl |
20/60 + 20/60= 2/3 |