Question

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.
A. 4/25

B. 4/35

C. 11/70

D. 6/35

Answer 1

3 black ribbons and 12 green ribbons
so P(Lila selects a black ribbon)=3/(3+12)
=1/5
2 black ribbons and 12 green ribbons left
P(Jessica selects a green ribbon)=12/(12+2)
=6/7

so P(Lila selects a black ribbon and Jessica selects a green ribbon)
=1/5*6/7
=6/35

ans is D

Answer 2

$\frac{3}{15} \times \frac{12}{14} \\ = \frac{36}{210} \\ = \frac{6}{35}$

Note:
3/15 because 3 black ribbons out of 15 total ribbons.
12/14 because 12 green ribbons out of 14 total ribbons after 1 ribbon is taken out, which makes 15-14=1

Answer is D.

Hope this helps. - M