Question

there are two bags containing white and black balls. in the first bag, there are 8 white and 6 black balls and in the second bag, there are 4 white and 7 black balls. one ball is drawn at random from any of these two bags. find the probability of this ball being black.

Answer 1

in first bag - white balls - 8
black balls-6
in second bag - white balls - 4
- black balls- 7
sum of all balls of both bag- 25
sum of white balls- 12
sum of black balls-13
P( black ball ) - sum of black balls / sum of all balls
= 13/25

Answer 2

Answer:

Probability is 41/77.

Step-by-step explanation:

We are given that,

Number of black balls in Bag 1 = 6

Number of white balls in Bag 1 = 8

⇒ Total number of balls in bag 1 = 6 + 8 = 14

Number of black balls in Bag 2 = 7

Number of white balls in Bag 2 = 4

⇒ Total number of balls in bag 2 = 7 + 4 = 11

A ball is drawn out from a bag. We need to find probability that ball is black.

$Probability=\frac{Number\:of\:favorable\:outcome}{Number\:of\:total\:outcome}$

First,  Probability of selection of both bags is equal = 1/2

Then,  Probability of black ball taken from bag 1 = (1/2) x (6/14)  = 3/14

Now,  Probability of black ball taken from bag 2 = (1/2) x (7/11)  = 7/22

Thus,

Probability of black ball = 3/14 + 7/22 = 41/77

Therefore, Probability of black ball is 41/77.