A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two balls drawn have different colours?
A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two balls drawn have different colours?
Show Hint
- \( \frac{2}{3} \)
- \( \frac{1}{3} \)
- \( \frac{1}{2} \)
- \( 1 \)
The Correct Option is A
Solution and Explanation
Step 1: Total number of ways to draw 2 balls from the 4 balls.
The total number of ways to choose 2 balls from 4 is given by the combination formula: \[ \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6 \] Thus, there are 6 possible outcomes when drawing two balls.
Step 2: Number of favourable outcomes (balls with different colours).
The favourable outcomes are the cases where one red ball and one blue ball are drawn. The number of ways to choose one red ball and one blue ball is: \[ \binom{2}{1} \times \binom{2}{1} = 2 \times 2 = 4 \] Thus, there are 4 favourable outcomes where the balls drawn are of different colours.
Step 3: Probability calculation.
The probability that the two balls drawn have different colours is given by the ratio of favourable outcomes to the total outcomes: \[ P({\text{different colours}}) = \frac{{\text{favourable outcomes}}}{{\text{total outcomes}}} = \frac{4}{6} = \frac{2}{3} \]
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