Question

Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?

They are independent because P(X) x P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) x P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).

Answer 1

The answer is C if im not mistaken

Answer 2

Answer: The correct option is

(A)
`P(X)* P(Y)=P(X\cap Y).`

Step-by-step explanation: We are given to consider a situation in which X and Y are two events such that

`P(X)=(4)/(5),~P(Y)=(1)/(4),~P(X\cap Y)=(1)/(5).`

We are to select the statement that best describes the events X and Y.

We know that

any two events A and B are said to be independent if

`P(A)* P(B)=P(A\cap B).`

We have, for events X and Y,

`P(X)* P(Y)=(4)/(5)*(1)/(4)=(1)/(5)=P(X\cap Y)\\\\\\\Rightarrow P(X)* P(Y)=P(X\cap Y).`

Thus, X and Y are independent because
`P(X)* P(Y)=P(X\cap Y).`

Option (A) is CORRECT.