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. 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)

Explanation:

Step1: Calculate P(A)

The total number of items is 400, and the number of plastic - bottles is 136. So, $P(A)=\frac{136}{400} = 0.34$.

Step2: Calculate P(A|B)

The number of items recycled by tenth - graders is 150, and the number of plastic - bottles recycled by tenth - graders is 40. So, $P(A|B)=\frac{40}{150}=\frac{4}{15}\approx0.27$.

Step3: Check independence

Two events A and B are independent if $P(A|B)=P(A)$. Since $P(A|B)\approx0.27$ and $P(A) = 0.34$, $P(A|B)
eq P(A)$. So A and B are not independent events.

Answer:

A and B are not independent events because $P(A|B)
eq P(A)$.