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

Step 1: Note the box composition.
The box has 1 red ball and 2 blue balls, so 3 balls in total.

Step 2: Use the "with replacement" rule.
Each ball goes back into the box after being drawn, so the box has the exact same 1 red and 2 blue balls before every single draw.
This means each draw is independent, and past outcomes do not change the odds of the next draw.

Step 3: Compute the probability for the third draw.
The information that the first two draws were blue does not change the box, so it does not change the probability for the third draw.
\[ P(\text{blue on draw 3}) = \frac{\text{number of blue balls}}{\text{total balls}} = \frac{2}{3} \]
Final Answer:
The probability of drawing a blue ball on the third draw is \( \dfrac{2}{3} \). \[ \boxed{\dfrac{2}{3}} \]