Question
A bag contains 4 red, 5 blue and 6 green balls. Two
balls are drawn at random without replacement. What is the probability that the two balls are of different colours?Solution
ATQ, Total balls = 4 + 5 + 6 = 15 Total ways to choose 2 balls = 15C2 = 105 Unfavourable cases: both same colour. Red–red: 4C2 = 6 Blue–blue: 5C2 = 10 Green–green: 6C2 = 15 Total same-colour = 6 + 10 + 15 = 31 So different colours: 105 − 31 = 74 Required probability = 74/105.
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