a prize bag contains four country music cds, eight pop music cds, and five classic rock cds. what is the…

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

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

Answer

Explanation:

Step1: Calculate total number of CDs

Total CDs = 4 (country) + 8 (pop) + 5 (classic rock) = 17

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

Probability of pulling a classic rock CD first, $P_1=\frac{5}{17}$

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

After pulling a classic rock CD, number of CDs left = 17 - 1 = 16

Step4: Calculate probability of pulling a country music CD second

Probability of pulling a country music CD second, $P_2=\frac{4}{16}$

Step5: Calculate the combined probability

The probability of both events happening is $P = P_1\times P_2=\frac{5}{17}\times\frac{4}{16}=\frac{5}{68}\approx0.07$

Answer:

0.07