Shelly has 5 yellow pens, 6 blue pens, and 9 green pens. She picks 1 pen at random and does not replace it. Then she picks another pen. Find the probability of: P(yellow then blue) P(2 yellow) P(2 green) P(green then blue) Show all your work for each of the probability problems above. (8 points)

Answer 1

Total number of pens = 5 (yellow) + 6 (blue) + 9 (green) = 20 pens

1. P(yellow then blue):
Number of ways to pick a yellow pen first = 5
Number of ways to pick a blue pen second = 6
Total number of ways to pick 2 pens = 20 * 19 = 380

P(yellow then blue) = (5/20) * (6/19) = 30/380 = 3/38

2. P(2 yellow):
Number of ways to pick 2 yellow pens = 5C2 = 10

P(2 yellow) = 10/190 = 1/19

3. P(2 green):
Number of ways to pick 2 green pens = 9C2 = 36

P(2 green) = 36/190 = 18/95

4. P(green then blue):
Number of ways to pick a green pen first = 9
Number of ways to pick a blue pen second = 6
Total number of ways to pick 2 pens = 20 * 19 = 380

P(green then blue) = (9/20) * (6/19) = 54/380 = 27/190