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 dice is cast.If the face 1 or 3 turns up, a ball is taken from the first bag and if any other face turns up a ball is chosen from the second bag. The probability of choosing a black ball is

• A. 11/21
• B. 10/21
• C. 12/21
• D. 9/21

Answer 1

The Correct Option is A

Bag1 = 3 back, 4 white balls
Bag2 = 4 black, 3 white balls
Probability of selecting bag 1 \(=\frac{2}{6}=\frac{1}{3}\)

Probability of selecting bag 2 \(=1-\frac{1}{3}=\frac{2}{3}\)

Probability of choosing a black ball from bag 1 \(=\frac{3}{7}\) 

Probability of choosing a black ball from bag 2 \(=\frac{4}{7}\) 

Required probability \(=\frac{1}{3}\times\frac{3}{7}+\frac{2}{3}\times\frac{4}{7}\) 

\(=\frac{11}{21}\).So the correct option is (A)