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A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps. If four caps are picked at random, what is the probability that two are red, one is blue and one is green?
- a)22/1001
- b)80/1001
- c)21/1001
- d)55/1001
Correct answer is option 'B'. 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 * 4c1 * 2c1 / 14c4 = 80/1001
Probability = 5c2 * 4c1 * 2c1 / 14c4 = 80/1001
Most Upvoted Answer
A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps...
Probability of picking two red, one blue, and one green cap:
Total number of ways to pick 4 caps:
- Total number of caps = 5 + 4 + 3 + 2 = 14
- Number of ways to pick 4 caps out of 14 = 14C4 = 1001
Number of ways to pick two red caps:
- Number of ways to pick 2 red caps out of 5 = 5C2 = 10
Number of ways to pick one blue cap:
- Number of ways to pick 1 blue cap out of 4 = 4C1 = 4
Number of ways to pick one green cap:
- Number of ways to pick 1 green cap out of 2 = 2C1 = 2
Probability calculation:
- Number of favorable outcomes = Number of ways to pick 2 red caps * Number of ways to pick 1 blue cap * Number of ways to pick 1 green cap = 10 * 4 * 2 = 80
- Probability = Number of favorable outcomes / Total number of ways to pick 4 caps = 80 / 1001 = 80/1001
Therefore, the probability that two caps are red, one is blue, and one is green is 80/1001, which corresponds to option 'b'.
Total number of ways to pick 4 caps:
- Total number of caps = 5 + 4 + 3 + 2 = 14
- Number of ways to pick 4 caps out of 14 = 14C4 = 1001
Number of ways to pick two red caps:
- Number of ways to pick 2 red caps out of 5 = 5C2 = 10
Number of ways to pick one blue cap:
- Number of ways to pick 1 blue cap out of 4 = 4C1 = 4
Number of ways to pick one green cap:
- Number of ways to pick 1 green cap out of 2 = 2C1 = 2
Probability calculation:
- Number of favorable outcomes = Number of ways to pick 2 red caps * Number of ways to pick 1 blue cap * Number of ways to pick 1 green cap = 10 * 4 * 2 = 80
- Probability = Number of favorable outcomes / Total number of ways to pick 4 caps = 80 / 1001 = 80/1001
Therefore, the probability that two caps are red, one is blue, and one is green is 80/1001, which corresponds to option 'b'.
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