Question

A bag contains 5 red marbles, 7 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be red?

Answer 1

$\displaystyle\\|\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\|A|=\binom{5}{2}=\dfrac{5!}{2!3!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{120}=\dfrac{1}{12}\approx0.083$