You are told that P(E) = 0.55, P(F) = 0.4, and P(E and F) = 0.28.  Are events E and F INDEPENDENT?  Justify your answer.  Be sure to refer to appropriate rules, definitions and properties.

To determine if events E and F are independent, we need to check if the probability of the intersection of E and F is equal to the product of their individual probabilities. In other words, we need to verify if:

$P(E \text{ and } F) = P(E) \times P(F)$

Given: $P(E) = 0.55$ $P(F) = 0.4$ $P(E \text{ and } F) = 0.28$

First, calculate the product of $P(E)$ and $P(F)$:

$P(E) \times P(F) = 0.55 \times 0.4 = 0.22$

Next, compare this result with $P(E \text{ and } F)$:

$P(E \text{ and } F) = 0.28$

Since $0.22 \neq 0.28$, the product of $P(E)$ and $P(F)$ is not equal to $P(E \text{ and } F)$.

Therefore, events E and F are not independent.