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

which statement is true about whether c and y are independent events? c and y are independent events because p(c | y)=p(y). c and y are independent events because p(c | y)=p(c). c and y are not independent events because p(c | y)≠p(y). c and y are not independent events because p(c | y)≠p(c).

which statement is true about whether c and y are independent events? c and y are independent events because p(c | y)=p(y). c and y are independent events because p(c | y)=p(c). c and y are not independent events because p(c | y)≠p(y). c and y are not independent events because p(c | y)≠p(c).

Answer

Explanation:

Step1: Calculate (P(C))

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

Step2: Calculate (P(C|Y))

The number of outcomes for event (Y) is (n(Y) = 75), and the number of outcomes for both (C) and (Y) is (n(C\cap Y)=35). By the formula for conditional - probability (P(C|Y)=\frac{P(C\cap Y)}{P(Y)}=\frac{n(C\cap Y)}{n(Y)}=\frac{35}{75}=\frac{7}{15}). Since (\frac{7}{15}\neq\frac{11}{30}), that is (P(C|Y)\neq P(C)).

Answer:

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