Topic: Engineering Mathematics
A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is
- A. $\frac{1}{90}$
- B. $\frac{1}{5}$
- C. $\frac{19}{90}$
- D. $\frac{2}{9}$
Answer: D. $\frac{2}{9}$
Explanation: Probability of first ball being red is $\frac{5}{10} = \frac{1}{2}$. Since there is no replacement, 9 balls are left (4 red). Probability of the second ball being red is $\frac{4}{9}$. Total probability $= \frac{1}{2} \times \frac{4}{9} = \frac{2}{9}$.