Question

Suppose a jar contains 8 red marbles and 25 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.

Answer 1

Answer: $\dfrac{7}{132}$

Step-by-step explanation:

Total marbles in the jar =  8+25 = 33

Using combinations, the number of ways of choosing two marbles out of 33=  $\dfrac{33!}{2!(33-2)!}\\\\=\dfrac{33!}{2\times31!}\\\\=\dfrac{33\times32}{2}=528$  (total outcomes)

Similarly, the number of ways of choosing two red marbles =

$\dfrac{8!}{2!6!}\\\\=\dfrac{8\times7}{2}=28$(favorable outcomes)

Required probability = $\dfrac{\text{favorable outcomes}}{\text{total outcomes}}$

$=\dfrac{28}{528}\\\\=\dfrac{7}{132}$

hence, required probability = $\dfrac{7}{132}$