Question

There are 3 red, 6 blue, 5 yellow, and 4 green hair bands in a bag. Morgan wants a blue hair band and a yellow hair band to wear to school. What is the probability of picking a yellow hair band followed by a blue hair band, if the first hair band drawn is not replaced?

Answer 1

To find the answer we need to use conditional probability:

`P(B\cap A)=P(A)P(B|A)`

In this case event A is picking a yellow band and event B is picking a blue band second.

Then:

`P(A)=(5)/(18)`

and:

`P(B|A)=(6)/(17)`

Then the probability we are looking for is:

`P(A\cap B)=(5)/(18)\cdot(6)/(17)=(5)/(51)`