Question

Information about the recycling drive at school is shown in the table. Let A be the event that the item pulled out of the recycling bin is a plastic bottle, and let B be the event that a tenth grader recycled that item.

A 5-column table has 4 rows. The first column has entries tenth grade, eleventh grade, twelfth grade, total. The second column is labeled aluminum cans with entries 80, 56, 64, 200. The third column is labeled glass bottles with entries 30, 9, 26, 65. The fourth column is labeled plastic bottles with entries 40, 45, 50, 135. The fifth column is labeled Total with entries 150, 110, 140, 400.

Which statement is true about whether A and B are independent events?

A and B are independent events because P(A∣B) = P(A).
A and B are independent events because P(A∣B) = P(B).
A and B are not independent events because P(A∣B) ≠ P(A).
A and B are not independent events because P(A∣B) ≠ P(B).

Answer 1

Answer:

A and B are not independent events because P(A∣B) ≠ P(A).

Step-by-step explanation:

Given

A: the item pulled out of the recycling bin is a plastic bottle

B: tenth grader recycled that item

number of plastic bottles recycled by a tenth grader: 40

Total number of plastic bottles: 135

Total items recycled by a tenth grader: 150

Total number of objects: 400

Then:

P(A) = 135/400  = 0.3375

Probability that a plastic bottles was recycled by a tenth grader:

P(A|B) = 40/150 = 0.2666

A and B are independent if P(A∣B) = P(A), which is not the case

Answer 2

Answer: C

Step-by-step explanation: