A bag contains 8 blue and 12 green balls. Two balls are drawn in succession without replacement. The probability that first is blue and second is green is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{24}{95}\)
The bag has 20 balls. By the multiplication rule, P(first blue and second green) = P(first blue) × P(second green, given the first was blue).
\(\displaystyle P(\text{first blue}) = \frac{8}{20}\)
After a blue ball is removed without replacement, 19 balls remain, 12 of them green:
\(\displaystyle P(\text{second green} \mid \text{first blue}) = \frac{12}{19}\)
\(\displaystyle P = \frac{8}{20} \times \frac{12}{19}\)
\(\displaystyle = \frac{24}{95}\)