Question

no additional details were added for this assignment.

let a represent drinking coffee and b represent drinking water.
which statement is true?

drinking coffee and drinking water are independent events because $p(a|b) = p(a)$ and $p(b|a) = p(b)$.
drinking coffee and drinking water are independent events because $p(a|b) \
eq p(a)$ and $p(b|a) \
eq p(b)$.
drinking coffee and drinking water are not independent events because $p(a|b) = p(a)$ and $p(b|a) = p(b)$.
drinking coffee and drinking water are not independent events because $p(a|b) \
eq p(a)$ and $p(b|a) \
eq p(b)$.

Explanation:

The definition of independent events is that the conditional probability of one event given the other equals the probability of the event itself, i.e., $P(A|B)=P(A)$ and $P(B|A)=P(B)$. The first option correctly states this definition for independence.

Answer:

A. Drinking coffee and drinking water are independent events because $P(A|B) = P(A)$ and $P(B|A) = P(B)$.