MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
An urn contains g green, b blue and y yellow balls. Three balls are drawn successively without replacement.
(1) Find the probability that exactly two of the three balls drawn are blue.
(2) Given that the third ball drawn is green, calculate the probability that exactly one of the first two balls drawn is blue.
(3) Suppose instead that b blue and n non-blue balls are in an urn and three balls are drawn without replacement. Derive a general expression for the probability that exactly two of the three drawn balls are blue in terms of b and n. State clearly any conditions on b and n required for your expression to be valid.