A box contains one red ball and two blue balls. One ball is drawn at random, its colour is noted and the ball is returned to the box. The process is repeated. In the first two draws, a blue ball appears each time. The probability of drawing a blue ball again in the third draw is
Options:
(A) 2/3
(B) 1/3
(C) 1/2
(D) 1
Official Answer Key:
A
Step-by-Step Solution & Explanation
Because the ball is replaced after every draw, the composition of the box (1 red + 2 blue) is identical before each draw. The draws are therefore independent events.
P(blue on 3rd draw | blue on 1st and 2nd) = P(blue) = 2/3
The information about the earlier draws is irrelevant — this is the classic “gambler’s fallacy” trap, and conditioning on past independent outcomes changes nothing.
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