Financial Risk Manager Part 1

Explanation

Let's define the events:

• Let A = {gets first question right}
• Let B = {gets second question right}

Given probabilities:

• P(A) = 0.4
• P(B) = 0.5
• P(A ∩ B) = 0.2 (probability of getting both questions correct)

We want to find P(A ∪ B) - the probability that she gets either the first OR the second question correct.

Using the addition rule of probability:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Substituting the given values:

P(A ∪ B) = 0.4 + 0.5 - 0.2 = 0.7

P(A ∪ B) = 0.4 + 0.5 - 0.2 = 0.7

Therefore, the probability that she gets either the first or the second question correct is 0.7.

Why this makes sense:

• If we simply added P(A) + P(B) = 0.4 + 0.5 = 0.9, we would be double-counting the cases where both questions are correct
• By subtracting P(A ∩ B) = 0.2, we remove this double-counting
• The result 0.7 represents the probability of getting at least one question correct