Answer:
C and Y are independent events because [tex]P(C|Y) = P(C)[/tex].
Step-by-step explanation:
Two events X and Y are independent only if
[tex]P(X\cap Y)=P(X)\times P(Y)[/tex]
Now, if C and Y are independent events, then
[tex]P(C\cap Y)=P(C)\times P(Y)[/tex]
Now, conditional probability of C given that Y has occurred is given as:
[tex]P(C|Y)=\frac{P(C\cap Y)}{P(Y)}\\P(C|Y)=\frac{P(C)\times P(Y)}{P(Y)}\\P(C|Y)=P(C)[/tex]
Therefore, two events C and Y are independent because [tex]P(C|Y) = P(C)[/tex]
