Financial Risk Manager Part 1
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An athlete takes part in two different events. The probability that she wins the first event is 0.3 and the probability that she wins the second event is 0.4. Given that the probability that she wins both events is 0.1, calculate the probability that she wins either the first, the second, or both events.
Other
Community
NNikitesh
A
0.2
B
0.5
C
0.6
D
0.1
Explanation:
Explanation
We are given:
- P(A) = Probability of winning first event = 0.3
- P(B) = Probability of winning second event = 0.4
- P(A ∩ B) = Probability of winning both events = 0.1
We want to find P(A ∪ B) = Probability of winning either the first, the second, or both events.
Using the addition rule of probability:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Substituting the given values:
P(A ∪ B) = 0.3 + 0.4 - 0.1 = 0.6
Therefore, the probability that she wins either the first, the second, or both events is 0.6.
This makes sense because:
- If we simply added P(A) + P(B) = 0.3 + 0.4 = 0.7, we would be double-counting the overlap (winning both events)
- Subtracting P(A ∩ B) = 0.1 corrects for this double-counting
- The result 0.6 represents the total probability of winning at least one event
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