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A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps. If three caps are picked at random, what is the probability that none is green?
- a)2/13
- b)3/13
- c)1/13
- d)5/13
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps...
Total caps = 14
Probability = 5c0 * 9c3/ 14c3 = 3/13
Probability = 5c0 * 9c3/ 14c3 = 3/13
Most Upvoted Answer
A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps...
Solution:
Total number of caps in the bag = 2 + 4 + 3 + 5 = 14
To find the probability of picking 3 caps at random and none of them being green, we need to find the number of ways in which we can pick 3 caps out of the 9 non-green caps in the bag.
Number of ways of picking 3 caps out of 9 = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84
To find the total number of ways of picking 3 caps out of 14, we need to find 14C3.
Number of ways of picking 3 caps out of 14 = 14C3 = (14 × 13 × 12)/(3 × 2 × 1) = 364
Therefore, the probability of picking 3 caps at random and none of them being green is:
84/364 = 3/13
Hence, the correct option is (B) 3/13.
Total number of caps in the bag = 2 + 4 + 3 + 5 = 14
To find the probability of picking 3 caps at random and none of them being green, we need to find the number of ways in which we can pick 3 caps out of the 9 non-green caps in the bag.
Number of ways of picking 3 caps out of 9 = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84
To find the total number of ways of picking 3 caps out of 14, we need to find 14C3.
Number of ways of picking 3 caps out of 14 = 14C3 = (14 × 13 × 12)/(3 × 2 × 1) = 364
Therefore, the probability of picking 3 caps at random and none of them being green is:
84/364 = 3/13
Hence, the correct option is (B) 3/13.
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Community Answer
A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps...
Total no of caps = 14.
Caps other than green = 9.
No of ways of selecting 3 such caps = 9C3.
No of ways of selecting 3 caps from all caps = 14C3.
Required probability = 9C3 / 14C3 = 3 / 13.
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