A bag contains 3 red and 5 blue balls. A second bag contains 5 red and 3 blue balls. Two balls are drawn randomly from the first bag and are put into the second bag without noticing their colours and then two balls are drawn from the second bag. Find the probability that the balls are blue and white. Share with your friends Share 0 Lovina Kansal answered this Dear student A red and blue ball can be drawn from the second bag in the following muyually exclusive ways:1) By transferrin 2 blue balls from first bag to the second bag and then drawing a red and a blue ball from it.2) By transferring 2 red balls from first bag to the second bag and then drawing a blue and a red ball from it.3) By transferring one blue and one red ball from first bag to secong bag and then drawing a blue and a red ball from it.Let E1,E2,E3 and A be the evnts as defined below:E1=two red balls are drawn from the first bag.E2=two blue balls are drawn from the first bag.E3=one blue and one red ball is drawn from the fiA= two balls drawn from the second bag are blue and red.We havePE1=3C28C2=514,PE2=5C28C2=328 and PE3=5C1×3C18C2=1528If E1 has already occured, that is, if two red balls have been transferred from thefirst bag to second bag, then the second bag will contain 3 blue and 7 red balls, therefore, the probability of drawing a blue and a red ball from the second bag is 3C1×7C110C2PA/E1=3C1×7C110C2=716Similarly, we have,P(A/E2)=5C1×5C110C2=59 and PA/E3=4C1×6C110C2=815By the law of total probability, we haveP(A)=P(E1)PA/E1+P(E2)P(A/E2)+PE3 PA/E3=328×715+514×59+1528×815=6731260 Regards 0 View Full Answer