Question

Uppose a jar contains 12 red marbles and 18 blue marbles. if you reach in the jar and pull out 2 marbles at random without replacement, (a) find the probability of getting two red marbles:

Answer 1

$\frac{12}{30} \times \frac{11}{29} = \frac{22}{145}$

Answer 2

$\displaystyle |\Omega|=\binom{30}{2}=\dfrac{30!}{2!28!}=\dfrac{29\cdot30}{2}=435\\ |A|=\binom{12}{2}=\dfrac{12!}{2!10!}=\dfrac{11\cdot12}{2}=66\\\\ P(A)=\dfrac{66}{435}=\dfrac{22}{145}\approx15\%$