Suppose there are two urns U1 AND U2. U1 contains two red balk and one green bal

Question

Suppose there are two urns U1 AND U2. U1 contains two red balk and one green ball, while U2 contains one red ball and two green ball. As turn s randomly selected, and then one ball is randomly selected form the urn. The ball is red. What is the probability that the urn selected was U1? An urn is randomly selected, and then two balk are randomly selected (without replacement) from the urn. The first ball is red and the second ball is green. What is the probability that the urn selected was U1? P(U1) = 2/3. P (U1) = 1/2

Explanation / Answer

a. From given information, P(U1)=P(U2)=1/2, P(G|U1)=1/3, P(R|U1)=2/3, P(G|U2)=2/3, P(R|U2)=1/3. Use Bayes theorem to find P(U1|R).

P(U1|R)=P(U1)*P(R|U1)/{P(U1)*P(R|U1)+P(U2)*P(R|U2)}

=1/2*2/3/(1/2*2/3+1/2*1/3)

=2/3 (ans)

b. There are two balls to be radomly selected from urns, urn 1 has 2 red and 1 green ball, and urn 2 has 1 red and 2 green balls. It is said that first ball has to be red followed by green ball. Therefore, probability of the urn selected is 1 is as follows.

P(U1)=1/2*2/3/(1/2*2/3+1/2*2/3)

=1/2

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