A bag contains hair ribbons for a spirit rally. The bag contains 3 black ribbons and 12 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that Lila selects a black ribbon and Jessica selects a green ribbon? Express your answer as a fraction in simplest form.

Accepted Solution

Total ribbons = 3 + 12 = 15
3/15 = black
12/15 = green

Therefore the probability Lila selects the black ribbon first is 12/15

Because Lila has taken one away, the total now decreases by one to 14
Therefore, there are 3/14 black ribbons now, and thus the probability that Jessica takes one is 3/14.

Then you just multiply the two together, so
12/15 x 3/14 = 36/210 = 6/35

So the final, simplified answer is 6/35