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