Question:
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?
Answer:
Total number of marbles in the box = 10+20+30 = 60
Red marbles = 10
Blue marbles = 20
Green marbles = 30
5 marbles are drawn from the box
1. Probability that all are blue = 20C5 / 60C5
= {20!/(5!*15!)}/{60!/(5!*55!)}
= (20!*55!)/(60!*15!)
2. Probability that at least one is blue = {20C1 *40C4 + 20C2 * 40C3 + 20C3 * 40C2 + 20C4 * 40C1 + 20C5 }/ 60C5
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