Question

There are 5 pink marbles and 4 orange marbles in a bag. Madison will randomly pick two marbles out of the bag without replacing the first marble chosen. What is the probability of Madison picking two orange marbles in a row?

Answer 1

In order to find the probability of both marbles being drawn being the same colour, the probability of each marble being drawn has to first be found and then multiply both probability to find the probability of two orange marble being drawn consecutively.

Now, the probability of drawing an orange marble = ⁴/₉

since a marble has been removed and wasn't replaced then there are now 5 pink + 3 orange marbles (8 marbles in total) in the bag.

∴ the probability of the second marble drawn being orange = ³/₈
⇒ the probability of two orange marbles in a row without the first being replaced = ⁴/₉ × ³/₈ = ¹/₆