Be sure you are writing out your steps. You will have to submit your shown work for each problem at the end Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles were properly dispensed. Correctly Placed Incorrectly Placed Plastic #2 8 5 Plastic #4 5 2 What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
To find the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle, we first need to calculate the total number of Plastic #4 bottles that were correctly placed. From the data provided, we see that there are 5 Plastic #4 bottles that were correctly placed.
Next, we calculate the total number of bottles in the sample. To do this, we add up the correctly placed and incorrectly placed bottles for each plastic type. So, for Plastic #2, there are 8 correctly placed bottles + 5 incorrectly placed bottles = 13 total Plastic #2 bottles. And for Plastic #4, there are 5 correctly placed bottles + 2 incorrectly placed bottles = 7 total Plastic #4 bottles.
Therefore, the total number of bottles in the sample is 13 + 7 = 20 bottles.
Now, we can calculate the probability of selecting a bottle that is both correctly placed and is a Plastic #4 bottle:
P(correctly placed and Plastic #4) = (Number of Plastic #4 bottles that are correctly placed) / (Total number of bottles in the sample)
P(correctly placed and Plastic #4) = 5 / 20
P(correctly placed and Plastic #4) = 1/4
P(correctly placed and Plastic #4) = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.