Which pair(s)of events is (are)independent? A and $ B $ given the following: $ P(A)=0.4, P(B)=0.3, P(A $ and $ B)=0.16 $ $ C $ and $ D $ given the following: $ P(C)=0.4, P(D)=0.3, P(C \mid D)=0.4 $

Question

Quizplus · Accepted Answer

For two events to be independent, the probability of both occurring together should be the product of their individual probabilities. For $A$ and $B$, $P(A \text{ and } B) = 0.16$, but $P(A)P(B) = 0.4 \times 0.3 = 0.12$, so they are not independent. For $C$ and $D$, $P(C \mid D) = P(C)$, which means the occurrence of $D$ does not affect the probability of $C$, indicating $C$ and $D$ are independent.

Which Pair(s)of Events Is (Are)independent? a And B B B Given the Following

Which Pair(s)of Events Is (Are)independent? a And $B$ Given the Following