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A bag contains 3 red balls and 8 blacks ball and another bag contains 5 red balls and 7 blacks balls, one ball is drawn at random from either of the bag, find the probability that the ball is red.
- a)93/264
- b)95/264
- c)91/264
- d)97/264
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A bag contains 3 red balls and 8 blacks ball and another bag contains ...
Probability = probability of selecting the bag and probability of selecting red ball
(1/2)(3/11) + (1/2)(5/12) = 91/264
Most Upvoted Answer
A bag contains 3 red balls and 8 blacks ball and another bag contains ...
Given:
- Bag 1 contains 3 red balls and 8 black balls
- Bag 2 contains 5 red balls and 7 black balls
- One ball is drawn at random from either of the bags
To find:
- Probability that the ball is red
Solution:
Let's first find the probability of selecting Bag 1 and Bag 2:
- Probability of selecting Bag 1 = 1/2 (since there are two bags and we are equally likely to select either of them)
- Probability of selecting Bag 2 = 1/2 (same reason as above)
Now, we can find the probability of selecting a red ball:
- Probability of selecting a red ball from Bag 1 = 3/11 (since there are 3 red balls and 11 total balls in Bag 1)
- Probability of selecting a red ball from Bag 2 = 5/12 (since there are 5 red balls and 12 total balls in Bag 2)
Using the Law of Total Probability, we can find the overall probability of selecting a red ball:
P(Red) = P(Bag 1) * P(Red from Bag 1) + P(Bag 2) * P(Red from Bag 2)
= (1/2) * (3/11) + (1/2) * (5/12)
= 33/264 + 55/264
= 88/264
= 11/33
= 0.3333
Therefore, the probability that the ball is red is 11/33 or 91/264.
Hence, option C is the correct answer.
- Bag 1 contains 3 red balls and 8 black balls
- Bag 2 contains 5 red balls and 7 black balls
- One ball is drawn at random from either of the bags
To find:
- Probability that the ball is red
Solution:
Let's first find the probability of selecting Bag 1 and Bag 2:
- Probability of selecting Bag 1 = 1/2 (since there are two bags and we are equally likely to select either of them)
- Probability of selecting Bag 2 = 1/2 (same reason as above)
Now, we can find the probability of selecting a red ball:
- Probability of selecting a red ball from Bag 1 = 3/11 (since there are 3 red balls and 11 total balls in Bag 1)
- Probability of selecting a red ball from Bag 2 = 5/12 (since there are 5 red balls and 12 total balls in Bag 2)
Using the Law of Total Probability, we can find the overall probability of selecting a red ball:
P(Red) = P(Bag 1) * P(Red from Bag 1) + P(Bag 2) * P(Red from Bag 2)
= (1/2) * (3/11) + (1/2) * (5/12)
= 33/264 + 55/264
= 88/264
= 11/33
= 0.3333
Therefore, the probability that the ball is red is 11/33 or 91/264.
Hence, option C is the correct answer.
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