Understanding Independent Events Practice Test

A website tracks visits. Let event $A$ be “a visit is from a mobile device” and event $B$ be “a visit results in a purchase.” Given that $P(A)=0.60$, $P(B)=0.20$, and $P(A\cap B)=0.15$, are $A$ and $B$ independent? Justify using probabilities by comparing $P(A\cap B)$ to $P(A)P(B)$.

A jar contains many marbles. One marble is selected at random. Let event $A$ be “the marble is red” and event $B$ be “the marble is large.” Given that $P(A)=0.30$, $P(B)=\tfrac{2}{5}$, and $P(A\cap B)=0.12$, are $A$ and $B$ independent? Justify using probabilities by comparing $P(A\cap B)$ to $P(A)P(B)$.