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The problem in the image involves calculating the probability that a vinyl record selected at random from a collection is from a specific decade. The collection has 40 records, distributed by decade as follows:

- 3 records from the 40s
- 6 records from the 50s
- 3 records from the 60s
- 4 records from the 70s
- 8 records from the 80s

The task is to determine the probability that a randomly selected record is from the 60s, as the probabilities for the 40s and 50s are given.

### Provided:
- Probability it’s from the 40s: \( \frac{3}{40} \)
- Probability it’s from the 50s: \( \frac{3}{20} \)

### Calculating the probability for the 60s:

There are 3 records from the 60s, and the total collection consists of 40 records. The probability \( P(60s) \) that a randomly selected record is from the 60s is calculated by dividing the number of records from the 60s by the total number of records:

\[
P(60s) = \frac{3}{40}
\]

So, the probability that a record is from the 60s is \( \frac{3}{40} \).

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Would you like further details on this? Here are some relative questions you could explore:

1. How can you calculate the probability for other decades in this collection?
2. What is the total probability of all decades combined, and how does it check out?
3. How would the probabilities change if another decade was added to the collection?
4. How can you express probabilities in percentage form?
5. How do you compare probabilities between decades?

**Tip:** To ensure your probabilities add up correctly, the sum of the probabilities for all possible outcomes should always equal 1.

Butch has a collection of 40 vinyl records from throughout the 20th century, including three from the 40s, six from the 50s, three from the 60s, four from the 70s, and eight from the 80s. What is the probability that a randomly selected record will be from each of the following decades?

Learn how to calculate the probability that a vinyl record selected at random from a collection of 40 is from a specific decade. The collection includes 3 records from the 40s, 6 from the 50s, 3 from the 60s, 4 from the 70s, and 8 from the 80s. This problem explores the basic principles of probability and fractions, suitable for students in Grades 6-8.

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