What is the probability that Chris gets an orange marble on his first draw and a purple marble on his second draw?

Question

Chris gas a marble jar that contains 10 orange marbles, and 9 purple marbles. He will draw two marbles from the jar one at a time without replacing the first marble. What is the probability that Chris gets an orange marble on his first draw and a purple marble on his second draw?

Answer 1

P(orange marble on first draw) = 10/19

Conditioned on first draw = orange marble, there will be 18 marbles left, 9 of which are purple

Therefore P(purple marble on second draw | orange marble on first draw) = 9/18

P(purple marble on second draw *and* orange marble on first draw) =

P(orange marble on first draw) * P(purple marble on second draw | orange marble on first draw) =

10*9/19*18 = 90/342 ≈ .26