Two balls are drawn from an urn containing 5 green, 3 blue, and 7 yellow balls one by one without replacement. What is the probability that at least one ball is blue? - Mathematics and Statistics

Sum

Two balls are drawn from an urn containing 5 green, 3 blue, and 7 yellow balls one by one without replacement. What is the probability that at least one ball is blue?

Solution

Total number of balls in the urn = 5 + 3 + 7 = 15

Out of these 12 are non-blue balls.
Two balls can be drawn from 15 balls without replacement in 15C2 = (15xx14)/(1xx2) = 105 ways
∴ n(S) =105
Let A be the event that at least one ball is blue.
i.e., 1 blue and other non-blue or both are blue.

∴ n(A) = 3C1 × 12C1 + 3C2
= 3 × 12 + 3
= 36 + 3
= 39

∴ P(A) = ("n"("A"))/("n"("S"))=39/105=13/35

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