- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 5. The Total Probability Rule

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**CFA Practice Question**

An individual has a 10% probability of suffering from a headache when he has a cold versus 1% when he does not have a cold. If the individual has a 5% probability of developing a cold, what is the probability that this individual suffers from a headache?

A. 1.45%

B. 2.23%

C. 11%

**Explanation:**Assume event A is the event in which the individual suffers from a headache. Using the total probability rule, P(A) = 0.1 x 0.05 + 0.01 x 0.95 = 1.45%.

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**User Contributed Comments**
3

User |
Comment |
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ana2 |
How do you come up with the .95? is it the .05 ( 100%-95%) because if he has a 5% chance of getting a cold, he will be 95 times more likely to have a headache? And if no to a cold, it will be 95 time more likely that he does not have a headache? |

ascruggs92 |
If you have a 5% chance of getting a cold, you have a 95% chance of not getting a cold. Therefore, the total probability of an individual developing a cold is the chance of them getting a cold and developing a headache (5% x 10%) plus the chance of them not getting a cold and developing a headache (95% x 1%) |

weebe |
A is individual suffers from headache B is individual suffers from cold P(A) = P(A and B) + P (A and not B) where P(A and B) = P(A | B) * P(B) P(A and not B) = P(A | not B) * P (not B) and given P(A | B) = 0.1 P(A | not B) = 0.01 |