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 132 1 over 32 10290 10 over 290 129 1 over 29 10320

Answer 1

To find the probability that Kyle will select a jazz CD first and then a country CD without replacement, we need to follow these steps:

1. **Count 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 CDs

2. **Calculate the probability of selecting a jazz CD first**:
- Probability of selecting a jazz CD = (number of jazz CDs) / (total number of CDs) = 3/30 = 1/10

3. **Calculate the total number of CDs left after one jazz CD is selected**:
- Total CDs remaining = 30 - 1 = 29 CDs

4. **Calculate the probability of selecting a country CD next**:
- Probability of selecting a country CD = (number of country CDs) / (total number of CDs remaining) = 10/29

5. **Multiply the probabilities of both events**:
\[
P(\text{jazz then country}) = P(\text{jazz}) \times P(\text{country after jazz}) = \left(\frac{3}{30}\right) \times \left(\frac{10}{29}\right) = \frac{1}{10} \times \frac{10}{29} = \frac{1}{29}
\]

Therefore, the probability that Kyle will select a jazz CD first and then a country CD is \( \frac{1}{29} \).

The correct response is \( \frac{1}{29} \).