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The problem shown asks for the probabilities that a randomly selected vinyl record from Butch's collection of 40 will come from various decades.

Let's go through the data given:
- 3 records from the 1940s
- 6 records from the 1950s
- 3 records from the 1960s
- 4 records from the 1970s
- 8 records from the 1980s

Total number of records = 40.

We are asked to calculate the probability of selecting a record from each decade, which is computed as:

\[
P(\text{decade}) = \frac{\text{number of records from the decade}}{\text{total records}}
\]

### Probabilities:
1. **1940s**: There are 3 records from the 1940s, so:
   \[
   P(\text{1940s}) = \frac{3}{40}
   \]

2. **1950s**: There are 6 records from the 1950s, so:
   \[
   P(\text{1950s}) = \frac{6}{40} = \frac{3}{20}
   \]

3. **1960s**: There are 3 records from the 1960s, so:
   \[
   P(\text{1960s}) = \frac{3}{40}
   \]

4. **1970s**: There are 4 records from the 1970s, so:
   \[
   P(\text{1970s}) = \frac{4}{40} = \frac{1}{10}
   \]

5. **1980s**: There are 8 records from the 1980s, so:
   \[
   P(\text{1980s}) = \frac{8}{40} = \frac{1}{5}
   \]

The missing value for the 1980s probability is \(\frac{1}{5}\).

Would you like any further details or clarification on this? 

Here are 5 questions to help deepen understanding:
1. What is the total sum of all probabilities, and why does it equal 1?
2. How would the probabilities change if one more record from the 1970s was added?
3. Can the probabilities be converted into percentages? If so, how?
4. How do you interpret these probabilities in the context of random selection?
5. What would happen to the probabilities if the total number of records increased but the distribution remained the same?

**Tip**: When calculating probabilities, always ensure the sum of all individual probabilities equals 1 to verify accuracy.

Butch has a collection of 40 vinyl records from the 1940s, 1950s, 1960s, 1970s, and 1980s. The task is to calculate the probability of randomly selecting a record from each of these decades.

Learn how to calculate the probability of selecting a vinyl record from the 1940s, 1950s, 1960s, 1970s, or 1980s out of a collection of 40 records. This problem demonstrates the use of basic probability and fractions.

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