Financial Risk Manager Part 1

Explanation

To calculate the probability that she wins either the first or the second event, we use the addition rule of probability for non-mutually exclusive events:

[ P(A \cup B) = P(A) + P(B) - P(A \cap B) ]

Where:

• ( P(A) = 0.3 ) (probability of winning first event)
• ( P(B) = 0.4 ) (probability of winning second event)
• ( P(A \cap B) = 0.1 ) (probability of winning both events)

Substituting the values: [ P(A \cup B) = 0.3 + 0.4 - 0.1 = 0.6 ]

Therefore, the probability that she wins either the first or the second event is 0.6.

Verification:

• The events are not mutually exclusive since ( P(A \cap B) = 0.1 \neq 0 )
• Without subtracting the intersection, we would get 0.7, which would overcount the overlap
• The correct answer accounts for the fact that winning both events is included in both individual probabilities