Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Explanation:

Let:
'A' be the event that an individual chosen at random comes from Africa.
'E' be the event that an individual chosen at random comes from Europe.
'S' be the event that an individual chosen at random comes from South America.
'L' be the event that an individual chosen at random submits tax returns late.

Now, we wish to determine $P(\text{Africa}|\text{Late}) = P(A|L)$

Applying Bayes Theorem,

P(A|L) = \frac{(P(A) \times P(L|A))}{[P(A) \times P(L|A) + P(E) \times P(L|E) + P(S) \times P(L|S)]}

= 0.6 \times \frac{0.45}{[(0.6 \times 0.45) + (0.2 \times 0.15) + (0.2 \times 0.20)]}

= \frac{0.27}{[0.27 + 0.03 + 0.04]}

= 0.7941

Explanation:

Now, we wish to determine $P(\text{Africa}|\text{Late}) = P(A|L)$

Applying Bayes Theorem,

P(A|L) = \frac{(P(A) \times P(L|A))}{[P(A) \times P(L|A) + P(E) \times P(L|E) + P(S) \times P(L|S)]}

= 0.6 \times \frac{0.45}{[(0.6 \times 0.45) + (0.2 \times 0.15) + (0.2 \times 0.20)]}

= \frac{0.27}{[0.27 + 0.03 + 0.04]}

= 0.7941

Comments (0)

No comments yet.

Q.61 The punctuality of filing tax returns is investigated by considering a number of citizens from different geographical regions. In the sample, 60% of respondents come from Africa, 20% from Europe, and 20% from South America. The probabilities of 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

RRohit

Last updated: June 22, 2026 at 14:25

0.7941.

0.0794.

0.34.

0.27.