Financial Risk Manager Part 1
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Q.3257 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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A
0.30
B
0.40
C
0.50
D
0.6
Explanation:
Explanation
Given:
- P(A) = Probability of reading Business News = 0.50
- P(B) = Probability of reading BloomField News = 0.40
- P(A ∩ B) = Probability of reading both = 0.30
Using the formula for union of two events:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A ∪ B) = 0.50 + 0.40 − 0.30 = 0.60
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.
Therefore, 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
P(neither) = 1 − P(A ∪ B) = 1 − 0.60 = 0.40
Answer: B (0.40)
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