Question

Bag 1 contains 3 red and 4 white balls and bag 2 contains 4 red and 5 white balls. two balls are drawn at random from bag 1 and transferred to bag 2. a ball is then drawn from bag 2 and is found to be red in colour. find the probability that the transferred balls were both white.

Answer 1

Given Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball drawn is red in color.

Let E1E1 be the event that a red ball is transferred from Bag I to Bag II, and E2E2 be the event that a black ball is transferred from Bag I to Bag II. Let A be the event that the ball drawn is red.

P(E1)=33+4=37P(E1)=33+4=37

P(E2)=44+3=47P(E2)=44+3=47

Step 2:

P(AE1)=510=12P(AE1)=510=12

P(AE2)=410=25P(AE2)=410=25

P(E2E)=P(EE2).P(E2)∑4i=1(P(EEi).P(Ei))P(E2E)=P(EE2).P(E2)∑i=14(P(EEi).P(Ei)).

⇒47×2537×12+47×25=1631