Question

There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.

Answer 1

so the answer is 11/21

Answer 2

Answer:

11/21

Step-by-step explanation:

There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls.

Let the Event is E1 to roll a dice and it shows 1 or 3; Probability P(E1)=1/3

Let the Event is E2 to roll a dice and it shows 2,4,5 or 6; Probability P(E1)=2/3

If dice shown 1 or 3,ball from 1st bag is taken out,probability of to be black colour P(B|E1)=3/7

If dice shows any other number,ball from 2st bag is taken out,probability of to be black colour P(B|E2)=4/7

probability of choosing a black ball=

P(E1)P(B|E1)+P(E2)P(B|E2)

$\frac{1}{3} \times \frac{3}{7} + \frac{2}{3} \times \frac{4}{7} \\ \\ = \frac{3}{21} + \frac{8}{21} \\ \\ = \frac{11}{21}$

Hope it helps you.