Question

There are three green bags and 2 red bags. In each of the three green bags there are 4 yellow and 12 blue balls. In each of the two red bags there are 12 yellow and 6 blue balls. A bag is picked at random, and from the chosen bag a ball is picked at random. Find the probability that the ball picked is yellow.​

Answer 1

12 red,9 green,8 blue,5 yellow

Total balls=34

i) probability of green ball=9/34

ii)probability of yellow ball=5/34

iii)probability of white ball=0/34=0

Answer 2

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We have been given that P(R|A)=58, P(Y|A)=38, P(R|B)=13, and P(Y|B)=23 .

If we choose a bag at random, then P(A)=P(B)=12.

Therefore, by the law of total probability, P(R)=P(R∩A)+P(R∩B)=P(A)P(R|A)+P(B)P(R|B)=12⋅58+12⋅13=2348 so P(A|R)=P(R∩A)P(R)=5/1623/48=1523.