Question

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

• A. \( \dfrac{2}{3} \)
• B. \( \dfrac{1}{3} \)
• C. \( \dfrac{1}{2} \)
• D. 1

Hint:

Remember the ball is returned to the box each time, so every draw is independent of the earlier ones.

Answer 1

The Correct Option is A

This question tests whether you can tell the difference between sampling with replacement and without replacement.

1. Option (A) $2/3$: correct, because returning the ball resets the box every time, so the third draw only depends on the box's fixed makeup of 1 red and 2 blue out of 3 balls.
2. Option (B) $1/3$: wrong, this would be the chance of drawing the red ball, not a blue one.
3. Option (C) $1/2$: wrong, this ratio does not match either the red or blue count against the total of 3 balls.
4. Option (D) $1$: wrong, this would only hold if the box held blue balls only, but a red ball is still sitting in there.

Because the ball is replaced after each draw, the first two blue draws carry no information about the third draw. The box always has 2 blue balls out of 3, so the answer stays $2/3$, option (A).