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.

Question

asked Dec 28, 2022 101k views

1 Answer

Factorypolaris · Answer 1 · 2023-01-03T02:16:48+0000

Answer:
(7)/(132)

Explanation:

Total marbles in the jar = 8+25 = 33

Using combinations, the number of ways of choosing two marbles out of 33=
$(33!)/(2!(33-2)!)\\\\=(33!)/(2*31!)\\\\=(33*32)/(2)=528$ (total outcomes)

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

$(8!)/(2!6!)\\\\=(8*7)/(2)=28$ (favorable outcomes)

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

$=(28)/(528)\\\\=(7)/(132)$

hence, required probability =
(7)/(132)