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