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Question
Solve the following:
An urn contains 5 red balls and 2 green balls. A ball is drawn. If its green, a red ball is added to the urn and if its red, a green ball is added to the urn. (The original ball is not returned to the urn). Then a second ball is drawn. What is the probability that the second ball is red?
Solution
A: Event of drawing a red ball and placing a green ball in the urn
B: Event of drawing a green ball and placing a red ball
C: Event of drawing a red ball in the second draw
P(A) = `5/7`, P(B) = `2/7, "P"("C"//"A") = 4/7, "P"("C"//"B") = 6/7`
Required probability
= P(C)
= `"P"("A") * "P"("C"//"A") + "P"("B") * "P"("C"//"B")`
= `5/7 xx 4/7 + 2/7 xx 6/7`
= `32/49`
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