billyjoebob19
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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).

Respuesta :

The answer is C if im not mistaken

Answer:  The correct option is

(A) [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]

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

[tex]P(X)=\dfrac{4}{5},~P(Y)=\dfrac{1}{4},~P(X\cap Y)=\dfrac{1}{5}.[/tex]

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

[tex]P(A)\times P(B)=P(A\cap B).[/tex]

We have, for events X and Y,

[tex]P(X)\times P(Y)=\dfrac{4}{5}\times\dfrac{1}{4}=\dfrac{1}{5}=P(X\cap Y)\\\\\\\Rightarrow P(X)\times P(Y)=P(X\cap Y).[/tex]

Thus, X and Y are independent because [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]

Option (A) is CORRECT.

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