Question

There are two bags a and b bag a contains 3 red balls and 4 black balls while that b contains 4 red and 5 black balls two balls drawn at random from bag a are transferred to bank be and then one ball is drawn from bagby find the probability that it is red ball

Answer 1

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