Financial Risk Manager Part 1
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The probability that a portfolio manager reads Business News weekly is 0.50, while the probability that a portfolio manager reads BloomField News is 0.40. If the probability that a portfolio manager reads both Business News and BloomField News is 0.30, then the probability that a portfolio manager does not read any of the two newspapers is closest to:
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NNikitesh
A
0.30.
B
0.40.
C
0.50.
D
0.6
Explanation:
Explanation
Let's define the events:
- Let A = event that a portfolio manager reads Business News weekly
- Let B = event that a portfolio manager reads BloomField News
Given:
- P(A) = 0.50
- P(B) = 0.40
- P(A ∩ B) = 0.30 (probability of reading both)
We need to find the probability that a portfolio manager does NOT read either newspaper, which is P(A' ∩ B') or 1 - P(A ∪ B).
Step 1: Calculate P(A ∪ B) Using the addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) P(A ∪ B) = 0.50 + 0.40 - 0.30 = 0.60
This means the probability that a portfolio manager reads at least one of the two newspapers is 0.60.
Step 2: Calculate the complement The probability that a portfolio manager does NOT read any of the two newspapers is: P(neither) = 1 - P(A ∪ B) = 1 - 0.60 = 0.40
Verification using Venn diagram approach:
- Probability of reading only Business News: P(A) - P(A ∩ B) = 0.50 - 0.30 = 0.20
- Probability of reading only BloomField News: P(B) - P(A ∩ B) = 0.40 - 0.30 = 0.10
- Probability of reading both: 0.30
- Total probability of reading at least one: 0.20 + 0.10 + 0.30 = 0.60
- Probability of reading neither: 1 - 0.60 = 0.40
Therefore, the correct answer is B) 0.40.
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