Question

A bag contains hair ribbons for a spirit rally. The bag contains 9 black ribbons and 6 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.

Answer 1

Option B.
`(9)/(35)`

Explanation:

A bag contains black ribbons = 9

Green ribbons = 6

Total ribbons = 9 + 6 = 15

First Lila selects a ribbon, the probability that Lila selects a black ribbon
`P_(1)` =
`(9)/(15)`

Then Jessica selects a ribbon without replacement so the probability that Jessica selects green ribbon
`P_(2)` =
`(6)/(14)`

P =
`P_(1)` ×
`P_(2)`

P =
`(9)/(15)` ×
`(6)/(14)` =
`(54)/(210)` =
`(9)/(35)`

The probability that Lila selects a black ribbon and Jessica selects a green ribbon is
`(9)/(35)`.