Question

There are 3 bags a,b,c. Bag a contain 2 white and 3 black, Bag a contains 4 white and 2 black, and Bag c contain 3 white and 2 black ball, respectively. A ball is drawn at random from randomly chosen bag then find the probability that it is a black ball

Answer 1

Correct question: There are 3 bags a,b,c. Bag a contain 2 white and 3 black, Bag b contains 4 white and 2 black, and Bag c contain 3 white and 2 black ball, respectively. A ball is drawn at random from randomly chosen bag then find the probability that it is a black ball.

Answer :

probability of picking the bag a  = $\frac{1}{3}$

probability of taking out black ball out of bag a =  $\frac{3}{5} \times \frac{1}{3}$

probability of picking the bag b = $\frac{1}{3}$  

probability of taking out black ball out of bag b =$\frac{2}{6} \times \frac{1}{3}$

probability of picking the bag c  = $\frac{1}{3}$

probability of taking out black ball out of bag c = $\frac{2}{5} \times \frac{1}{3}$

Hence the probability  of taking black ball from one of the three bag =$\frac{3}{5} \times \frac{1}{3}+\frac{2}{6} \times \frac{1}{3} +\frac{2}{5} \times \frac{1}{3}$

= 4\9

Thus the the probability that ball drawn is a black ball is $\frac{4}{9}$

Answer 2

Answer:

Step-by-step explanation:

Given :-

Bag A contains = 2 white and 3 black Balls

Bag B contains = 4 white and 2 black Balls

Bag C contains = 3 white and 2 black Balls

To Find :-

The probability that ball drawn is black ball.

Solution :-

Probability of picking the bag A  =  1/3

Probability of taking out black ball out of bag A =  3/5 × 1/3

Probability of picking the bag B = 1/3  

Probability of taking out black ball out of bag B =  2/6 × 1/3

Probability of picking the bag C  =  1/3

Probability of taking out black ball out of bag C = 2/5 × 1/3

Probability  of taking black ball from one of the three bag = 3/5 × 1/3 + 2/6 × 1/3 + 2/5 × 1/3 = 4/9

Hence, The probability that ball drawn is black ball is 4/9.