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. correctly placed incorrectly placed plastic #2 4 2 plastic #4 3 2 what is the probability that a randomly selected bottle is made of plastic #2 given that the bottle is incorrectly placed? simplify any fractions.
Answer
Explanation:
Step1: Find number of incorrectly - placed bottles
The number of incorrectly - placed plastic #2 bottles is 2 and the number of incorrectly - placed plastic #4 bottles is 2. So the total number of incorrectly - placed bottles is $2 + 2=4$.
Step2: Find number of incorrectly - placed plastic #2 bottles
The number of incorrectly - placed plastic #2 bottles is 2.
Step3: Calculate the conditional probability
The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event that the bottle is plastic #2 and $B$ is the event that the bottle is incorrectly placed, then $P(A|B)=\frac{\text{Number of plastic #2 and incorrectly placed}}{\text{Number of incorrectly placed}}$. So the probability is $\frac{2}{4}=\frac{1}{2}$.
Answer:
$\frac{1}{2}$