A bag contains 5 white, 7 red and 3 black balls. If two balls are drawn one by one without replacement, then the probability that at least one ball is black, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{13}{35} \)
“At least one black” is the complement of “no black ball”. There are 12 balls that are not black, out of 15:
\( \displaystyle P(\text{no black})=\frac{{}^{12}C_{2}}{{}^{15}C_{2}} \)
\( \displaystyle =\frac{66}{105}=\frac{22}{35} \)
\( \displaystyle P(\text{at least one black})=1-\frac{22}{35}=\frac{13}{35} \)