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Curious about people's recycling behaviors, Franco put on some gloves and sifted through some recycling and trash bins. He kept count of the plastic type of each bottle and which bottles are properly dispensed. Correctly placed Incorrectly placed Plastic #2 3 Plastic #4 3 3 What is the probability that a randomly selected bottle is made of plastic #2 or is correctly placed? Simplify any fractions.

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Solution

Note: The event here is Mutually Exclusive,, meaning the 2 events can happen at the same time

Total number = 4 + 3 + 3+3 = 13

[tex]\begin{gathered} P\mleft(A\mright)+P\mleft(B\mright)-P\mleft(AnB\mright) \\ \frac{7}{13}\text{ + }\frac{7}{13}-\frac{4}{13} \\ \frac{7+7-4}{13} \\ \frac{10}{13} \end{gathered}[/tex][tex]F\text{inal Answer = }\frac{10}{13}\text{ }[/tex]

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