Question

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 are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work. Plastic #2 correctly placed: 8 incorrectly placed: 5 Plastic #4 correctly placed: 5 incorrectly placed: 2

A)13/20
B)7/20
C)5/8
D)1/4

Answer 1

To calculate the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle, we first need to determine the total number of Plastic #4 bottles, both correctly and incorrectly placed.

Total number of Plastic #4 bottles = 5 (correctly placed) + 2 (incorrectly placed) = 7

Next, we calculate the total number of correctly placed bottles:

Total number of correctly placed bottles = 5 (Plastic #4) + 8 (Plastic #2) = 13

Therefore, the probability of selecting a bottle that is correctly placed AND is a Plastic #4 bottle is:

Probability = (Number of desired outcomes) / (Total number of outcomes)
Probability = 5 (number of correctly placed Plastic #4 bottles) / 13 (total number of correctly placed bottles)

Probability = 5/13

So, the answer is:

A) 13/20