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? express your answer in decimal form, rounded to the nearest hundredth. 0.03 0.07 0.15 0.18

Explanation:

Step1: Calculate total number of CDs

The total number of CDs is $4 + 8+5=17$.

Step2: Calculate probability of first - pulling a classic rock CD

The probability of pulling a classic rock CD first is $\frac{5}{17}$ since there are 5 classic rock CDs out of 17 total CDs.

Step3: Calculate probability of second - pulling a country music CD

After pulling a classic rock CD without replacement, there are 16 CDs left. The probability of pulling a country music CD is $\frac{4}{16}$.

Step4: Calculate the combined probability

The probability of both events happening is the product of the two probabilities, so $P=\frac{5}{17}\times\frac{4}{16}=\frac{20}{272}\approx 0.07$.

Answer:

0.07