Question

Two balls are selected from two black and two red balls. The probability that the two balls will have no black ball is:

• A. \( \frac{1}{7} \)
• B. \( \frac{1}{5} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{1}{3} \)
• E. \( \frac{1}{6} \)

Hint:

For sequential selection: \( \frac{2}{4} \times \frac{1}{3} = \frac{1}{6} \). Both methods give the same result.

Answer 1

Answer: (E)

Concept: “No black ball” means both selected balls must be red. Probability: \[ P = \frac{\text{Favorable ways}}{\text{Total ways}} \]

Step 1: Find total number of ways.
Total balls: \[ 2 \text{ black} + 2 \text{ red} = 4 \] Ways to choose 2 balls: \[ \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6 \]

Step 2: Find favorable ways.
To get no black ball, select both balls from red balls: \[ \binom{2}{2} = 1 \]

Step 3: Calculate probability.
\[ P = \frac{1}{6} \]

Step 4: Final answer.
\[ \boxed{\frac{1}{6}} \]