Problem

Butch has a collection of 80 vinyl records from throughout the 20 th century including nine from the 40 s, four from the $50 \mathrm{~s}$, eleven from the $60 \mathrm{~s}$, eight from the $70 \mathrm{~s}$, and 16 from the $80 \mathrm{~s}$. If he randomly selects one from his collection of 80 , find the probability it will be from each of the following decades.

The probability that it is from the $40 \mathrm{~s}$ is $\square$. (Type an integer or a simplified fraction.)

Answer

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Answer

Final Answer: The probability that the record is from the 40s is \( \boxed{\frac{9}{80}} \) or \( \boxed{0.1125} \).

Steps

Step 1 :Butch has a collection of 80 vinyl records from throughout the 20 th century including nine from the 40 s, four from the $50 \mathrm{~s}$, eleven from the $60 \mathrm{~s}$, eight from the $70 \mathrm{~s}$, and 16 from the $80 \mathrm{~s}$. If he randomly selects one from his collection of 80 , find the probability it will be from each of the following decades.

Step 2 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the event is selecting a record from the 40s and the total number of outcomes is the total number of records.

Step 3 :So, we need to divide the number of records from the 40s by the total number of records.

Step 4 :The number of records from the 40s is 9 and the total number of records is 80.

Step 5 :The probability that the record is from the 40s is \( \frac{9}{80} \) or 0.1125.

Step 6 :Final Answer: The probability that the record is from the 40s is \( \boxed{\frac{9}{80}} \) or \( \boxed{0.1125} \).

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