GATE | Gate IT 2005 | Question 1

A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is
(A) 1/36
(B) 1/6
(C) 1/4
(D) 1/3


Answer: (B)

Explanation: As number of colors is 3,Possible combinations -> 3! = 6

Probability of Blue  marble: 10/60

Probability of Green  marble: 20/60

Probability of Red marble: 30/60

Probability that no two of the marbles drawn have the same colour is = 6 * (10/60 * 20/60 * 30/60) = 1/6

Therefore B is the Answer

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