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?

Answer 1

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`