Question

One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red

Answer 1

hope it will help you

Answer 2

Solution:

Probability of drawing a red ball from first bag P(R)=3/8

Probability of drawing a black ball from first bag P(B)=5/8

Now if one ball taken out from bag 1 is of red colour ,then probability of drawing a red ball from bag 2, P(R')=7/11

Now if one ball taken out from bag 1 is of black colour ,then probability of drawing a red ball from bag 2, P(R'')=6/11

Total probability of getting a red ball from second bag =

P(R)P(R')+P(B)P(R'')

$\frac{3}{8} \times \frac{7}{11} + \frac{5}{8} \times \frac{6}{11} \\ \\ = \frac{21}{88} + \frac{30}{88} \\ \\ = \frac{51}{88}$