One box contains five red balls and four green balls, and a second box contains

Question

One box contains five red balls and four green balls, and a second box contains six red balls and three green balls. A ball is randomly chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box. What is the probability that a red ball is selected from the first box and a red ball is selected from the second box? Put all balls back into their original positions and repeat the selection process. At the conclusion of the selection process, what is the probability that the numbers of red and green balls in the first box are identical to the numbers in the beginning?

Explanation / Answer

A)as if first red ball is chosen from first box to second box, the second box will have 10 balls out of which 7 are red.

PROBABility that a red ball is selected from the first box and a red ball is selected from the second box

=(5/9)*(7/10)=7/18

b)probabilty that are identical as per beginning=P(red from first box*red from second box+green from first*green from second) =(5/9)*(7/10)+(4/9)*(4/10)=51/90=17/30

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