A store sells both new and used parts; 60% in stock are....

[lea8802]

A parts store sells both new and used parts. Sixty percent of the parts in stock are used. Sixty-one percent are used or defective. If 5 percent of the store's parts are defective, what percentage are both used and defective?

How would you come up with the solution?

 

[soroban]

Re: Probability

Hello, lea8802!

A parts store sells both new and used parts.
Sixty percent of the stock is Used.
Five percent of the stock is Defective.
Sixty-one percent is Used or Defective.

What percentage are both Used and Defective?

Formula: \(\displaystyle \;\;\;n(U\,\cup\,D) \;=\;n(U)\,+\,n(D)\,-\,n(U\,\cap\,D)\)

We have: \(\displaystyle \;\;\;\;61\%\;\;\:\,=\;60\%\;+\;5\%\;-\;n(U\,\cap\,D)\)

Therefore: \(\displaystyle \:n(U\,\cap\,D) \;=\;60\%\,+\,5\%\,-\,61\%\;=\;4\%\)

 

[lea8802]

Probability

Thank you. You were a huge help.