SOLUTION: An urn contains 3 red balls and 7 green balls. A ball is drawn randomly and in its place are put 2 of the opposite color. Then another ball is drawn randomly. Find the conditional

Question 1026168: An urn contains 3 red balls and 7 green balls. A ball is drawn randomly and in its place are put 2 of the opposite color. Then another ball is drawn randomly. Find the conditional probability that the first ball was green given that the second ball is red.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
We have to find P(G1|R2) = P(G1 ∩ R2)/P(R2).
By the law of total probability,
P(R2) = P(G1 ∩ R2)+P(R1 ∩ R2) = P(R2|G1)P(G1) + P(R2|R1)P(R1)
=
==>P(G1|R2) = P(G1 ∩ R2)/P(R2) = .

RELATED QUESTIONS
An urn contains red balls and 3 green balls. A ball is drawn randomly and 6 more of the... (answered by robertb)

An urn contains 5 red balls and 3 green balls. A ball is drawn randomly and 6 more of the (answered by robertb)

an urn contains 12 balls identical in every respect except color. there are 3 red balls,... (answered by checkley77)

An urn contains 5 yellow balls and 4 green balls. A ball is drawn randomly; it is not put (answered by robertb)

An urn contains 3 red and 4 green balls. 4 balls are drawn, one after another subject to... (answered by Fombitz,Edwin McCravy)

Question 1 - Consider two urns. Urn 1 contains 4 red balls and 2 white balls, and urn 2... (answered by solver91311,Natolino1983)

Urn 1 contains 6 red balls and 5 black balls. Urn 2 contains 3 red balls and 3 black... (answered by Boreal)

An urn contains two red balls and two green balls. A ball is drawn randomly. If the ball... (answered by Natolino1983)

Let urn 1 contains 4 red balls and 2 white balls, and let the urn 2 contain 3 balls of... (answered by harpazo)