A bag contains 10 white and 15 black balls . 2 balls are drawn without replacement. The probability that first is white & second is black, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{1}{4} \)
The draws are without replacement, so the second probability is conditional on the first.
The probability that the first ball is white is \( \frac{10}{25} \). Then 24 balls remain, of which 15 are black, so the probability that the second is black is \( \frac{15}{24} \):
\( \displaystyle P=\frac{10}{25}\times\frac{15}{24} \)
\( \displaystyle =\frac{2}{5}\times\frac{5}{8}=\frac{1}{4} \)
Tip: Using 25 balls again in the second draw (as if with replacement) gives \( \frac{10}{25}\times\frac{15}{25}=\frac{6}{25} \), which is Option (2).