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.

Question

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

1029010 over 290

1032010 over 320

1291 over 29

132

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. Determine the total number of CDs:

   • There are 10 country CDs,
   • 5 rock CDs,
   • 12 hip hop CDs,
   • 3 jazz CDs.

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

2. Calculate the probability of selecting a jazz CD first:

   • There are 3 jazz CDs out of 30 total CDs.
   • Probability of selecting a jazz CD = \( P(\text{jazz}) = \frac{3}{30} = \frac{1}{10} \).

3. Calculate the probability of selecting a country CD second (after selecting a jazz CD):

   • After selecting one jazz CD, there are now 29 CDs left (30 - 1 = 29).
   • There are still 10 country CDs remaining.
   • Probability of selecting a country CD after selecting a jazz CD = \( P(\text{country} | \text{jazz}) = \frac{10}{29} \).

4. Calculate the combined probability of both events: \[ P(\text{jazz and then country}) = P(\text{jazz}) \times P(\text{country} | \text{jazz}) = \frac{1}{10} \times \frac{10}{29} = \frac{1 \times 10}{10 \times 29} = \frac{10}{290}. \]

5. Reduce the fraction: \[ \frac{10}{290} = \frac{1}{29}. \]

The reduced probability that Kyle will select a jazz CD and then a country CD is \( \frac{1}{29} \).

From the given responses, it appears that the closest match is:

1291 over 29.