Financial Risk Manager Part 1
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The punctuality of filing tax returns has been investigated by considering a number of citizens in different geographical regions. In the sample, 60% of respondents were from Africa, 20% from Europe, and 20% South America. The probabilities of the late filing of returns in Africa, Europe, and South America are 45%, 15%, and 20% respectively.
If a late submitter is picked at random from the area under study, what is the probability that they are from Africa?
Other
Community
NNikitesh
A
0.7941
B
0.0794
C
0.34
D
0.27
Explanation:
This is a Bayes' Theorem application problem. Let's define the events:
- A: Individual is from Africa
- E: Individual is from Europe
- S: Individual is from South America
- L: Individual submits tax returns late
Given probabilities:
- P(A) = 0.60 (60% from Africa)
- P(E) = 0.20 (20% from Europe)
- P(S) = 0.20 (20% from South America)
- P(L|A) = 0.45 (45% late filing in Africa)
- P(L|E) = 0.15 (15% late filing in Europe)
- P(L|S) = 0.20 (20% late filing in South America)
We need to find P(A|L) - probability that someone is from Africa given they filed late.
Using Bayes' Theorem: P(A|L) = [P(A) × P(L|A)] / [P(A) × P(L|A) + P(E) × P(L|E) + P(S) × P(L|S)]
Numerator: 0.60 × 0.45 = 0.27 Denominator: (0.60 × 0.45) + (0.20 × 0.15) + (0.20 × 0.20) = 0.27 + 0.03 + 0.04 = 0.34
P(A|L) = 0.27 / 0.34 = 0.7941
Therefore, the probability that a randomly selected late submitter is from Africa is 0.7941 or approximately 79.41%.
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