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 the total number of CDs

The total number of CDs is \(4 + 8+5=17\).

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

The probability of pulling out a classic - rock CD first is \(P(\text{classic rock})=\frac{5}{17}\).

Step3: Calculate the number of CDs left after pulling out a classic - rock CD

After pulling out a classic - rock CD, the number of CDs left is \(17 - 1=16\).

Step4: Calculate the probability of pulling out a country music CD second

The probability of pulling out a country music CD second is \(P(\text{country}|\text{classic rock})=\frac{4}{16}\).

Step5: Calculate the probability of the two - step event

By the multiplication rule for dependent events \(P(A\cap B)=P(A)\times P(B|A)\), the probability is \(\frac{5}{17}\times\frac{4}{16}=\frac{20}{272}\approx0.07\).

Answer:

0.07