which statement is true about whether c and y are independent events? c and y are independent events because…

Answer:

C and Y are not independent events because (P(C|Y)\neq P(C)).

Explanation:

Step1: Recall independence formula

Two events (C) and (Y) are independent if (P(C|Y)=P(C)).

Step2: Calculate (P(C))

The total number of outcomes is (n = 300), and the number of outcomes in event (C) is (n_C=110). So (P(C)=\frac{110}{300}=\frac{11}{30}).

Step3: Calculate (P(C|Y))

The number of outcomes in (Y) is (n_Y = 75), and the number of outcomes in both (C) and (Y) is (n_{C\cap Y}=35). By the formula (P(C|Y)=\frac{P(C\cap Y)}{P(Y)}), and since (P(C\cap Y)=\frac{35}{300}), (P(Y)=\frac{75}{300}), then (P(C|Y)=\frac{\frac{35}{300}}{\frac{75}{300}}=\frac{35}{75}=\frac{7}{15}).

Step4: Compare probabilities

Since (\frac{7}{15}\neq\frac{11}{30}), i.e., (P(C|Y)\neq P(C)), (C) and (Y) are not - independent events.