A basket contains 4 red, 5 blue and 3 green marbles. If 2 marbles are drawn at random, what is the probability that both are red?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{1}{11}\)
Two marbles drawn together form a selection, so count with combinations: the ways of picking 2 red marbles out of all the ways of picking any 2.
Total number of marbles: \(4+5+3=12\)
Ways to pick any 2: \({}^{12}C_{2}=66\)
Ways to pick 2 red: \({}^{4}C_{2}=6\)
Probability that both are red: \(\displaystyle\frac{6}{66}=\frac{1}{11}\)