There are two bags containing white and black balls . In the first bag there…
2024
There are two bags containing white and black balls . In the first bag there are 6 white and 8 black balls and in the second bag, there are 4 white and 6 black balls . One ball is drawn at random from any of these two bags . Find the probability of this ball being black .
- A.
3/11
- B.
7/15
- C.
21/77
- D.
41/70
Attempted by 387 students.
Show answer & explanation
Correct answer: D
Answer: 41/70
Explanation:
Each bag is equally likely to be chosen, so the probability of choosing a bag is 1/2.
Probability of drawing a black ball from the first bag = 8/(6+8) = 8/14 = 4/7.
Probability of drawing a black ball from the second bag = 6/(4+6) = 6/10 = 3/5.
Total probability = 1/2*(4/7) + 1/2*(3/5) = 1/2*(20/35 + 21/35) = 1/2*(41/35) = 41/70.