Probability = the number of ways of achieving success. the total number of possible outcomes.

For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

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 ∩ 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 ∩ B)

We have, for events X and Y,

P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)

P(X) × P(Y) = P(X ∩ Y)

Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)

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The complete question is –

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: aStep-by-step explanation:The correct option is(A) P(X) × P(Y) = P(X ∩ Y)What is probability and example?Probability= the number of ways of achieving success. the total number of possible outcomes.probabilityof flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We writeP(heads) = ½ .events X and YindependentifP(X) × P(Y) = P(X ∩ Y)probabilitybrainly.com/question/27703806#SPJ4The complete question is –