Question

Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and 3 jazz CDs. What is the probability that Kyle will select a jazz CD from the box, and then, without replacing the CD, select a country CD? Reduce the fraction. (1 point) Responses 10290 10 over 290 10320 10 over 320 132 1 over 32 129

Answer 1

To find the probability that Kyle selects a jazz CD first and then a country CD without replacement, we can break down the problem into two steps:

1. **Calculate the total number of CDs.**
- Country CDs: 10
- Rock CDs: 5
- Hip hop CDs: 12
- Jazz CDs: 3

Total CDs = 10 + 5 + 12 + 3 = 30

2. **Calculate the probability of selecting a jazz CD.**
Probability of selecting a jazz CD = (Number of jazz CDs) / (Total number of CDs)
= 3 / 30
= 1 / 10

3. **Calculate the probability of selecting a country CD after a jazz CD has been selected.**
After selecting a jazz CD, there are now 29 CDs left (30 - 1), and the number of country CDs remains 10.
Probability of selecting a country CD = (Number of country CDs) / (Total remaining CDs)
= 10 / 29

4. **Calculate the combined probability.**
The combined probability of both events occurring (selecting a jazz CD first and then a country CD) is:
Probability = (Probability of selecting a jazz CD) * (Probability of selecting a country CD)
= (1/10) * (10/29)
= 10/290

5. **Reduce the fraction.**
10/290 can be reduced by dividing the numerator and denominator by 10:
= 1/29

Thus, the final answer for the probability that Kyle will select a jazz CD and then a country CD is **1/29**.