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 $\frac{9}{80}$. (Type an integer or a simplified fraction.)
The probability that it is from the $50 \mathrm{~s}$ is $\frac{1}{20}$. (Type an integer or a simplified fraction.)
The probability that it is from the $60 \mathrm{~s}$ is $\square$. (Type an integer or a simplified fraction.)

Answer

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Answer

Final Answer: The probability that a randomly selected vinyl record from Butch's collection is from the 60s is \( \boxed{\frac{11}{80}} \).

Steps

Step 1 :Butch has a collection of 80 vinyl records from throughout the 20th century including nine from the 40s, four from the 50s, eleven from the 60s, eight from the 70s, and 16 from the 80s. 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 that it is from the 40s is \( \frac{9}{80} \).

Step 3 :The probability that it is from the 50s is \( \frac{4}{80} = \frac{1}{20} \).

Step 4 :The question is asking for the probability that a randomly selected vinyl record from Butch's collection is from the 60s. 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 60s, and there are 11 such records. The total number of outcomes is the total number of records in Butch's collection, which is 80.

Step 5 :So, the probability is \( \frac{11}{80} \).

Step 6 :Final Answer: The probability that a randomly selected vinyl record from Butch's collection is from the 60s is \( \boxed{\frac{11}{80}} \).

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