Question

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

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 E1 be the event that a red ball is transferred from Bag I to Bag II, and E2 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)=3/3+4=3/7

P(E2)=4/4+3=4/7

Step 2:

P(A/E1)=5/10=1/2

P(A/E2)=4/10=2/5

P(E2/E)=P(E/E2).P(E2)            /   ∑4i=1(P(E/Ei).P(Ei)).

⇒47×2537×12+47×25=1631i=1(P(EEi).P(Ei)).

⇒4/7×2/5   / 3/7×1/2 + 4/7×2/5=16/31

hope this helps you :)