# Oranges are supplied from 3 parishes in Jamaica.C,M and A with probabilities P(C)=0.5,P(M)=0.1 and P(A)=0.4. Suppose that some oranges have a particular disease D such that P(D/C)=0.10,P(D/A)=0.25....

Oranges are supplied from 3 parishes in Jamaica.C,M and A with probabilities P(C)=0.5,P(M)=0.1 and P(A)=0.4.

Suppose that some oranges have a particular disease D such that P(D/C)=0.10,P(D/A)=0.25.

What is the probability that if an orange selected at random from a combined supply is found to have the disease,it is from A?

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If a diseased orange is found from the combined supply, there is a 2/3 chance that the orange is from A.

This is based on the following:

1.  For C:

P(C) = 0.5 and P(D/C) = 0.1

Therefore, if an orange is picked at random from the supply, the chance that it is diseased and from "C" is:

0.5 * 0.1 = 0.05

2.  Now for A:

P(A) = 0.4 and P(D/A) = 0.25

Again, if an orange is picked at random, the chance that it is diseased and from "A" is:

0.4 * 0.25 = 0.10

3.  The chance of a diseased orange being selected is:

P(D) = 0.05 + 0.10 = 0.15

4.  Therefore, if a diseased orange is found, the probability that it is from A is

P (A/D) = 0.10 / 0.15 = 2/3.  Answer

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