Discussion
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, blue ball appears each time. The probability of drawing blue ball again in the third draw is
Answer: A
The probability is \(\frac{2}{3}\).
The ball is put back after every draw, so the box always holds 1 red and 2 blue balls and each draw is independent of the earlier ones. The fact that blue came up twice changes nothing:
\[ P(\text{blue on draw 3}) = \frac{2}{3} \]
\(\frac{1}{3}\) is the chance of red. \(\frac{1}{2}\) treats the two colours as equally likely, and 1 assumes blue must repeat. A tempting slip is to compute \((2/3)^{3} = 8/27\), the chance of three blues in a row, but the question asks only about the third draw given the first two.
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