Question

Let A and B be events of a sample space.

Part (a) Suppose that A and (not B) are mutually exclusive. Explain why B occurs when A occurs.

Part (b) Suppose that B occurs whenever A occurs Explain why A and (not B) are mutually exclusive.

Short answer

Part (a).$Aand\left(notB\right)$are opposed to each other. It means that if $A$occurs, $B$does not, and vice versa. As a result, $B$occurs everytime $A$does.

If $A$occurs, then $B$occurs, i.e. $(notB)$does not occurs. As a result,$Aand(notB)$occur it happens at the same time. As a result, they are mutually exclusive.

Step-by-step solution

Part (a) Step 1. Given information.

Let $A$and $B$be sample space events. Let's pretend they're mutually exclusive.

Part (a) Step 2. Calculation.

$Aand\left(notB\right)$are opposed to each other. It means that if $A$occurs, $B$does not, and vice versa. As a result, $B$occurs everytime$A$does.

Part (b) Step 1. Given information.

Let $A$and $B$be sample space events. Assume that $B$occurs at the same time as $A$.

Part (b) Step 2. Calculation.

If $A$occurs, then $B$occurs, i.e. localid="1651140056335" $(notB)$does not occurs. As a result,localid="1651140065800" $Aand(notB)$occur it happens at the same time. As a result, they are mutually exclusive.