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Answer: 25%
The addition rule of probability is used to solve this question: Let: - P(E) = 0.18 (the probability that the Eurozone economy will grow is 18%) - P(M) = 0.52 (the probability that the ECB will loosen the monetary policy is 52%) - P(E ∩ M) = 0.45 (the joint probability that Eurozone economy will grow and the ECB will loosen its monetary policy is 45%) The probability that either the Eurozone economy will grow or the central bank will loosen its monetary policy: P(E ∪ M) = P(E) + P(M) - P(E ∩ M) = 0.18 + 0.52 - 0.45 = 0.25 = 25% This follows the general addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Author: Nikitesh Somanthe
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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 52%. Assuming that the joint probability that the Eurozone economy will grow and the ECB will loosen its monetary policy is 45%, then the probability that either the Eurozone economy will grow or the ECB will loosen its monetary policy is closest to:
A
42.12%
B
25%
C
11%
D
17.11%
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