Explanation:
We need to find the probability that a randomly picked late submitter is from Africa. This can be solved using Bayes' Theorem.
Let A = Africa, E = Europe, S = South America, and L = Late filing.
The given probabilities are: P(A) = 0.60 P(E) = 0.20 P(S) = 0.20
The conditional probabilities of late filing are: P(L|A) = 0.45 P(L|E) = 0.15 P(L|S) = 0.20
We need to calculate P(A|L). According to Bayes' Theorem: P(A|L) = [P(L|A) * P(A)] / P(L)
First, calculate the total probability of late filing, P(L): P(L) = P(L|A)*P(A) + P(L|E)*P(E) + P(L|S)*P(S) P(L) = (0.45 * 0.60) + (0.15 * 0.20) + (0.20 * 0.20) P(L) = 0.27 + 0.03 + 0.04 = 0.34
Now, calculate P(A|L): P(A|L) = (0.45 * 0.60) / 0.34 P(A|L) = 0.27 / 0.34 ≈ 0.7941
Thus, the probability that the late submitter is from Africa is 0.7941.
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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?
A
0.7941.
B
0.0794.
C
0.34.
D
0.27.