GATE 2021 BT – Question 31
Blue, green and red balls are transferred successively from A to B in that order. The probability of their reverse transfer to A in the same order (two decimal places) is _______.
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Correct answer: 0.16 to 0.18
Explanation
The balls are transferred from A to B in the order blue, green, red. They are then transferred back, one at a time, and we want them to return in the same order.
**Assumption.** When the balls are returned from B, every possible ordering of the three balls is equally likely.
**Number of orderings** of 3 distinct balls: $3!=6$.
**Favourable:** only one ordering is blue, green, red.
$$P=\frac16=0.1667\approx\mathbf{0.17}.$$