Bag I contains 4 red and 2 green balls and Bag II contains 3 red and 5 green balls. One ball is transferred at random from Bag I to Bag II and then a ball is drawn at random from Bag II. The ball so drawn is found to be green in colour. Find the probability that the transferred ball is also gr
Answer (1)
Student Expert
13th Feb, 2022
Hello Gautam,
Let us consider A1 is the events that a red ball is transferred from a bag I to Bag II and A2 Event is that green ball is transferred from the bag I to Bag II.
P(A1) = 4/6 & P(A2) = 2/6
Assume B be the event that the ball drawn from Bag is Green.
(1) when a Green ball is transferred.
P(B/A1) = 6/9
(2) when a Red ball is transferred.
P(B/A2) = 5/9
Now, P(A2/B) = [P(B/A2) × P(A2)] ÷ [(P(A1) × P(B/A2)) + (P(A2) × P(B/A1)]
Similarly, P(A2/B) = [((2/6) × (6/9)) ÷ ((4/6) × (5/9)) + ((2/6) × (6/9))]
= 3/8
Probability that the ball drawn fromBag I to Bag II is 3/8.
Hope this information was useful to you.
Good Luck!!
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