A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble…
2005
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
Attempted by 5 students.
Show answer & explanation
Correct answer: B
Total marbles = 10 + 20 + 30 = 60. Therefore P(blue) = 10/60 = 1/6, P(green) = 20/60 = 1/3 and P(red) = 30/60 = 1/2.
The marble is replaced after each draw, so the probabilities remain the same for all three draws. For no two marbles to have the same colour in three draws, the colours must be blue, green and red in some order.
Probability of one fixed order, say BGR, is (1/6)(1/3)(1/2) = 1/36. There are 3! = 6 possible orders.
Required probability = 6 × 1/36 = 1/6.