If three caps are picked at random, what is the probability that two are red and one is green?

Q: If three caps are picked at random, what is the probability that two are red and one is green?

Total number of caps = 12 ∴ n(S) = 12C3 = 220 n(E1) = Out of 4 red caps, number of ways to pick 2 caps = 4C2 = 6 n(E2) = Out of 5 green caps Number of ways to pick one cap = 5C1 = 5 P(E) = n(E1) x n(E2)/n(S) = (6 x 5)/220 = 3/22

9/22
6/19
1/6
3/22

Correct Answer: 3/22

Explanation:

Total number of caps = 12
∴ n(S) = ¹²C₃ = 220
n(E₁) = Out of 4 red caps, number of ways to pick 2 caps = ⁴C₂ = 6
n(E₂) = Out of 5 green caps
Number of ways to pick one cap = ⁵C₁ = 5
P(E) = n(E₁) x n(E₂)/n(S) = (6 x 5)/220 = 3/22

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