Chapter 10, Problem 8CT

To determine

Toexplain:

Necessity to subtract $P\left(AorB\right)$ when the events $A$ and $B$ are overlapping and disjoint.

Answer to Problem 8CT

For the overlapping events it is necessity to subtract $P\left(AorB\right)$ and for disjoints is not require to subtract $P\left(AorB\right)$ in $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$ .

Explanation of Solution

Given information:

Equation:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Formula used:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

The formula to get the $P\left(AorB\right)$ is as follows:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Two events are overlapping when they have one or more outcomes in common.

For two overlapping events, $A$ and $B$ , it is necessary to subtract $P\left(AandB\right)$ in equation $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$ while deriving $P\left(AorB\right)$ .

Two disjoints are disjoint or mutually exclusive when they have no outcomes in common. Thus, it is not required to subtract $P\left(AandB\right)$ in equation $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$ when deriving $P\left(AorB\right)$ .