Question

True or False. Justify
If two events A and B are mutually exclusive, they are not dependent.

Answer 1

Answer on Question #46508 – Math – Statistics and Probability

Question. True or False. Justify.

If two events $A$ and $B$ are mutually exclusive, they are not dependent.

Solution.

**Definition 1.** Events $A$ and $B$ are independent if $P(A \cap B) = P(A) \cdot P(B)$.

**Definition 2.** Events $A$ and $B$ are mutually exclusive if $P(A) + P(B) = 1$ and $P(A \cap B) = 0$.

We shall apply these definitions to our case. Let $P(A) = p \neq 0$. Note that events $A$ and $B$ are mutually exclusive $\Rightarrow P(A) + P(B) = 1$ and $P(A \cap B) = 0$. Then $P(B) = 1 - p$ and we have

$P(A \cap B) = 0 \neq p(1 - p) = P(A) \cdot P(B) \Rightarrow$ the statement is false.

Answer. False.

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