Question

If two balls are drawn from a bag having 5 red, 4 black and 6 blue balls, then probability of getting both the balls of different colour is:

• A. 74/105
• B. 15/68
• C. 53/68
• D. 31/105

Hint:

Calculating the complement (same color) is often faster than summing all different color pairs.

Answer 1

The Correct Option is A

Step 1: Concept
Probability of complementary events.

Step 2: Analysis
Total balls = $5 + 4 + 6 = 15$. Total ways to draw 2 balls = $\binom{15}{2} = \frac{15 \times 14}{2} = 105$.
$P(\text{different}) = 1 - P(\text{same colour})$.

Step 3: Calculation
Ways to get same colour = $\binom{5}{2} + \binom{4}{2} + \binom{6}{2} = 10 + 6 + 15 = 31$.
$P(\text{same}) = \frac{31}{105}$.
$P(\text{different}) = 1 - \frac{31}{105} = \frac{74}{105}$.

Step 4: Conclusion
The probability is 74/105. Final Answer: (A)