information about the recycling drive at school is shown in the table. let a be the event that the item…

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.\n| |aluminum cans|glass bottles|plastic bottles|total|\n|--|--|--|--|--|\n|tenth grade|80|30|40|150|\n|eleventh grade|56|9|45|110|\n|twelfth grade|64|26|50|140|\n|total|200|65|135|400|\nwhich statement is true about whether a and b are independent events?\na and b are independent events because p(a | b)=p(a).\na and b are independent events because p(a | b)=p(b).\na and b are not independent events because p(a | b)≠p(a).\na and b are not independent events because p(a | b)≠p(b).

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.\n| |aluminum cans|glass bottles|plastic bottles|total|\n|--|--|--|--|--|\n|tenth grade|80|30|40|150|\n|eleventh grade|56|9|45|110|\n|twelfth grade|64|26|50|140|\n|total|200|65|135|400|\nwhich statement is true about whether a and b are independent events?\na and b are independent events because p(a | b)=p(a).\na and b are independent events because p(a | b)=p(b).\na and b are not independent events because p(a | b)≠p(a).\na and b are not independent events because p(a | b)≠p(b).

Answer

Explanation:

Step1: Recall the definition of independent events

Two events (A) and (B) are independent if (P(A|B)=P(A)). The conditional - probability (P(A|B)) is the probability of event (A) occurring given that event (B) has occurred.

Step2: Calculate (P(A))

The total number of items is (400). The number of plastic bottles is (135). So (P(A)=\frac{135}{400}=\frac{27}{80}).

Step3: 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}). Since (\frac{4}{15}\neq\frac{27}{80}), that is (P(A|B)\neq P(A)).

Answer:

A and B are not independent events because (P(A|B)\neq P(A)).