Answer: 0.6

## 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

Author: Nikitesh Somanthe