- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 2. Unconditional, Conditional, and Joint Probabilities

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**CFA Practice Question**

Country A is a favorite for the final soccer match. However, country B has a stronger chance of making it to the final if country A wins its semi-final match. The probability that both A and B make it to the final is estimated at 30% and the probability of that country A reaches the final is 60%. What is the conditional probability of country B making it to the final if country A wins its semi-final match?

A. 50%

B. 90%

C. 18%

**Explanation:**P(A&B) = P(A|B) x P(B)

Prob(Country B in final|Country A is in final) = Prob(Countries A and B in final)/Prob(Country A in final) = 0.30/0.60 = 0.50, or 50%.

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**User Contributed Comments**
2

User |
Comment |
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stefanov11 |
I dont think the person who wrote that question has ever seen one game of football (soccer as you call it) . :-) |

Kevdharr |
Another way to look at it is this: It tells you that Country A has a 60% chance of making it to the final. So, P(A) = 0.60. It tells you that the JOINT PROBABILITY of both Country A AND B making the final is 30%. So P(A&B) = 0.30. We know that, in order to get the joint probability, you multiply the probability of A by the probability of B occurring. So P(A) * P(B) = P(A&B). Since we are given 2 of the 3 in this question, you can just solve algebraically to get P(B) = 0.50. |