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A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps.If three caps are picked at random, what is the probability that two are red and one is green?
- a)22/55
- b)15/81
- c)10/91
- d)5/91
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps...
Total caps = 14
Probability = 5c2 * 2c1/ 14c3 = 5/91
Probability = 5c2 * 2c1/ 14c3 = 5/91
Most Upvoted Answer
A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps...
Problem: A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps. If three caps are picked at random, what is the probability that two are red and one is green?
Solution:
Total number of caps in the bag = 5 + 4 + 3 + 2 = 14
Number of ways to pick three caps out of 14 = 14C3 = (14*13*12)/(3*2*1) = 364
Number of ways to pick two red caps out of 5 = 5C2 = (5*4)/(2*1) = 10
Number of ways to pick one green cap out of 2 = 2C1 = 2
Therefore, number of ways to pick two red caps and one green cap = 10*2 = 20
Probability of picking two red caps and one green cap = (Number of ways to pick two red caps and one green cap) / (Number of ways to pick three caps out of 14)
= 20/364
= 5/91
Hence, the probability that two caps are red and one is green is 5/91.
Answer: Option D (5/91)
Solution:
Total number of caps in the bag = 5 + 4 + 3 + 2 = 14
Number of ways to pick three caps out of 14 = 14C3 = (14*13*12)/(3*2*1) = 364
Number of ways to pick two red caps out of 5 = 5C2 = (5*4)/(2*1) = 10
Number of ways to pick one green cap out of 2 = 2C1 = 2
Therefore, number of ways to pick two red caps and one green cap = 10*2 = 20
Probability of picking two red caps and one green cap = (Number of ways to pick two red caps and one green cap) / (Number of ways to pick three caps out of 14)
= 20/364
= 5/91
Hence, the probability that two caps are red and one is green is 5/91.
Answer: Option D (5/91)
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Community Answer
A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps...
Total caps = 14
Probability = 5c2 * 2c1/ 14c3 = 5/91
Probability = 5c2 * 2c1/ 14c3 = 5/91
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