Question

A prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs. What is the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD?

Answer 1

`(5)/(68)`

Explanation:

We have been given that a prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs.

Total number of possible outcomes
`4+8+5=17`.

The probability of pulling out a classic rock CD would be
`(5)/(17)`.

Since the replacement is not allowed, so total number of CD's would be 1 less than 17 that is 16.

The probability of pulling out a country music CD would be
`(4)/(16)`.

Now to find the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD, we will multiply both probabilities as:

`(5)/(17)* (4)/(16)`

`(5)/(17)* (1)/(4)`

`(5)/(17* 4)`

`(5)/(68)`

Therefore, the probability of pulling out a classic rock CD and then, pulling out a country music CD without replacing it is
`(5)/(68)`.