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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 two balls are drawn at random (without replacement) from Bag II. The balls so drawn are found to be both red in colour. Find the probability that the transferred ball is red.

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 two balls are drawn at
random (without replacement) from Bag II. The balls so drawn are found to be
both red in colour. Find the probability that the transferred ball is red.

Grade:upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Let E1 : transferred ball is red.
E2 : transferred ball is black.
A : Getting both red from 2nd bag (after transfer)
P(E1)=3/7,P(E2)=4/7
P(A/E1) = 5c2/10c2=2/9
,P(A/E2) = 4c2/10c2=2/15
P(E1/A) = ((P(E1) P(A|E1))/ P(E1)P(A|E1)+P(E2)P(A|E2)
= 5/9
Thanks and Regards
Shaik Aasif
askIITians faculty

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