Financial Risk Manager Part 1
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The probability that the Eurozone economy will grow this year is 18%, and the probability that the European Central Bank (ECB) will loosen its monetary policy is 26%. Assuming that the joint probability that the Eurozone economy will grow and the ECB will loosen its monetary policy is 12%, then the probability that either the Eurozone economy will grow or the ECB will loosen its monetary policy is closest to:
Explanation:
Explanation
This question uses the addition rule of probability to find the probability of either event E or event M occurring.
Given:
- P(E) = 0.18 (probability Eurozone economy will grow)
- P(M) = 0.26 (probability ECB will loosen monetary policy)
- P(E∩M) = 0.12 (joint probability both events occur)
Formula:
The addition rule states: P(E ∪ M) = P(E) + P(M) - P(E∩M)
Calculation:
P(E ∪ M) = 0.18 + 0.26 - 0.12 = 0.32
Result:
The probability that either the Eurozone economy will grow OR the ECB will loosen its monetary policy is 32%.
Why this works:
- When we add P(E) and P(M), we double-count the intersection P(E∩M)
- We subtract P(E∩M) to avoid this double-counting
- This gives us the probability of at least one of the events occurring