- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Probability Trees and Conditional Expectations
- Subject 2. Probability Trees and Conditional Expectations
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%.
User Contributed Comments 3
| User | Comment |
|---|---|
| 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 |