Answer to Question #123451 in Statistics and Probability for Yasini

Question

There are two bags,one bag contains 4 white and 2 black balls, second bag contains 5 white and 4 black balls. 2 balls are transferred from the first bag to the second bag, then one ball is taken from the second bag. Find the probability that it is a white ball.

Answer 1

There are three ways in which 2 balls can be transferred from the first bag to second bag.

1)the balls transferred are both white its probability is

C_4,2/C_6,2=0.4

The second bag then contains 7 white and 4 black balls. The probability of drawind a white ball is 7/11. Combined probability of both steps=(2/5)*(7/11)=14/55

2)the balls transferred are both black its probability is

C_2,2/C_6,2=1/15

The second bag then contains 5 white and 6 black balls. The probability of drawind a white ball is 5/11. Combined probability of both steps=(1/15)*(5/11)=1/33

3)One black and one white balls are transferred. its probability is

C_4,1*C_2,1/C_6,2=8/15

The second bag then contains 6 white and 5 black balls. The probability of drawind a white ball is 6/11. Combined probability of both steps=(8/15)*(6/11)=16/55

The required probability is

P=14/55+1/33+16/55=19/33=0.576