Question

Consider a situation in which p(x) = and p(y) = . if p(x and y) is = , which best describes the events? they are independent because p(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) · p(y) = p(x and y). they are dependent because p(x) p(y) = p(x and y).

Answer 1

Considering the given probabilities, it is found that the correct option about whether the events are independent is given as follows:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

What are independent events?

Two events, A and B are independent, if:

$P(A \cap B) = P(A)P(B)$

Researching this problem on the internet, the probabilities are given as follows:

$P(X) = \frac{4}{5}, P(Y) = \frac{1}{4}, P(X \cap Y) = \frac{1}{5}$

Hence:

$P(X)P(Y) = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} = P(X \cap Y)$

Hence the events are independent and the correct option is given by:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

More can be learned about probabilities at https://brainly.com/question/14398287

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