some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted…

some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles. plastic #2 plastic #4 correctly placed 4 3 incorrectly placed 4 2 what is the probability that a randomly selected bottle is incorrectly placed or is made of plastic #2? simplify any fractions.

some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles. plastic #2 plastic #4 correctly placed 4 3 incorrectly placed 4 2 what is the probability that a randomly selected bottle is incorrectly placed or is made of plastic #2? simplify any fractions.

Answer

Explanation:

Step1: Calculate total number of bottles

Add all values in the table: $4 + 3+4 + 2=13$.

Step2: Calculate number of incorrectly - placed bottles

$4 + 2=6$.

Step3: Calculate number of plastic #2 bottles

$4 + 4=8$.

Step4: Calculate number of incorrectly - placed plastic #2 bottles

$4$.

Step5: Use the formula for $P(A\cup B)$

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of an incorrectly - placed bottle and $B$ is the event of a plastic #2 bottle. So $P(A)=\frac{6}{13}$, $P(B)=\frac{8}{13}$, and $P(A\cap B)=\frac{4}{13}$. Then $P(A\cup B)=\frac{6 + 8-4}{13}=\frac{10}{13}$.

Answer:

$\frac{10}{13}$