Question

Event A, Event B, and Event C are provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the complement of Event A [Find P(A')] ?Be sure to show your work and/or explain your reasoning.

Answer 1

If two events are mutually exclusive this means they cannot occur at the same time and do not over lap

If two events are mutually inclusive this means they can occur at the same time and they over lap

Event A and Event B are mutually exclusive

Event A and event C are not mutually exclusive

To find the complement of event A (A'), which is the part of the universal set of events not in A

We use the formula

`1\text{ - P(A)}=P(A^(\prime))`

P(A) = 0.45

substituting this into the equation yields

`\begin{gathered} 1-\text{ 0.45 = P(A')} \\ P(A^(\prime))\text{ = 0.55} \end{gathered}`

P(A') = 0.55