Question

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 1

Answer:

C and Y are independent events because $P(C|Y) = P(C)$.

Step-by-step explanation:

Two events X and Y are independent only if

$P(X\cap Y)=P(X)\times P(Y)$

Now, if C and Y are independent events, then

$P(C\cap Y)=P(C)\times P(Y)$

Now, conditional probability of C given that Y has occurred is given as:

$P(C|Y)=\frac{P(C\cap Y)}{P(Y)}\\P(C|Y)=\frac{P(C)\times P(Y)}{P(Y)}\\P(C|Y)=P(C)$

Therefore, two events C and Y are independent because $P(C|Y) = P(C)$

Answer 2

Answer:

D

Step-by-step explanation:

did the test and got 100%