Financial Risk Manager Part 1
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If A = P(wins first event) and B = P(wins second event), then we are told: P(A) = 0.3; P(B) = 0.4; and P(A ∩ B) = 0.1. We want P(A ∪ B).
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Explanation:
Explanation
To find P(A ∪ B), we use the formula for the probability of the union of two events:
[ P(A \cup B) = P(A) + P(B) - P(A \cap B) ]
Given:
- P(A) = 0.3
- P(B) = 0.4
- P(A ∩ B) = 0.1
Substituting the values: [ P(A \cup B) = 0.3 + 0.4 - 0.1 = 0.6 ]
Therefore, the probability that the team wins at least one of the two events is 0.6.
Key Concepts:
- Union Probability: The probability that at least one of the events occurs
- Intersection Probability: The probability that both events occur simultaneously
- Inclusion-Exclusion Principle: Accounts for the overlap between events to avoid double-counting
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