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.\n| |correctly placed|incorrectly placed|\n|--|--|--|\n|plastic #2|5|7|\n|plastic #4|2|8|\n|plastic #5|17|9|\nwhat is the probability that a randomly selected bottle is made of plastic #5 given that the bottle is correctly placed?\nsimplify any fractions.

some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles.\n| |correctly placed|incorrectly placed|\n|--|--|--|\n|plastic #2|5|7|\n|plastic #4|2|8|\n|plastic #5|17|9|\nwhat is the probability that a randomly selected bottle is made of plastic #5 given that the bottle is correctly placed?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total correctly - placed bottles

$5 + 2+17=24$

Step2: Identify number of correctly - placed plastic #5 bottles

The number of correctly - placed plastic #5 bottles is 17.

Step3: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In this case, the probability that a bottle is plastic #5 given it is correctly placed is $\frac{\text{Number of correctly - placed plastic #5 bottles}}{\text{Total number of correctly - placed bottles}}=\frac{17}{24}$

Answer:

$\frac{17}{24}$