Chapter 5.2, Problem 2.3CYU

To determine

To explain:The event $AorB$ and the probability of $P\left(AorB\right)$

Explanation of Solution

Given:

  $\begin{array}{l}P\left(AorB\right)\ne P\left(A\cup B\right)\\ P\left(AorB\right)\ne P\left(A\right)+P\left(B\right)\end{array}$

Concept used:

Definition of addition theorem of probability:- let A and B are two events of a random experiment and interested to find out the probability A or B

Then use the addition theorem of probability

Calculation:

let A and B are two events of a random experiment

use the addition theorem of probability

That is $\begin{array}{l}P\left(AorB\right)=P\left(A\cup B\right)\\ P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\end{array}$

If A and B are not mutually exclusive events

So,$P\left(A\cap B\right)\ne 0$

  $P\left(AorB\right)\ne P\left(A\right)+P\left(B\right)$

Therefore,

The event $AorB$ and the probability of $P\left(AorB\right)$

  $\ne P\left(A\right)+P\left(B\right)$