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A box contains 3 blue caps, 5 red caps, 4 green caps and 1 yellow cap, If two caps are picked at random, what is the probability that one is green and one is red?
- a)12/29
- b)10/39
- c)29/39
- d)6/11
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Problem: A box contains 3 blue caps, 5 red caps, 4 green caps, and 1 yellow cap. Two caps are picked at random. Find the probability that one is green and one is red.
Solution:
Total number of caps = 3 + 5 + 4 + 1 = 13
Let A be the event of picking a green cap and B be the event of picking a red cap.
Number of ways of picking one green cap out of 4 = 4C1 = 4
Number of ways of picking one red cap out of 5 = 5C1 = 5
Total number of ways of picking two caps out of 13 = 13C2 = (13 x 12) / 2 = 78
Number of ways of picking one green cap and one red cap = 4 x 5 = 20
Therefore, P(A and B) = (number of ways of picking one green cap and one red cap) / (total number of ways of picking two caps)
= 20 / 78
= 10 / 39
Hence, the probability that one cap is green and one cap is red is 10/39.
Answer: Option B
Solution:
Total number of caps = 3 + 5 + 4 + 1 = 13
Let A be the event of picking a green cap and B be the event of picking a red cap.
Number of ways of picking one green cap out of 4 = 4C1 = 4
Number of ways of picking one red cap out of 5 = 5C1 = 5
Total number of ways of picking two caps out of 13 = 13C2 = (13 x 12) / 2 = 78
Number of ways of picking one green cap and one red cap = 4 x 5 = 20
Therefore, P(A and B) = (number of ways of picking one green cap and one red cap) / (total number of ways of picking two caps)
= 20 / 78
= 10 / 39
Hence, the probability that one cap is green and one cap is red is 10/39.
Answer: Option B
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