Chapter 9.7, Problem 56E

To determine

To find the probability of the event that will happen.

Answer to Problem 56E

The probability that the event will happen is 0.11.

Explanation of Solution

Given:

  $P\left(E^{\prime }\right)=0.89$

Concept used:

Probability of a complement:

Let A be an event and A' be its complement. If the probability of A is $P\left(\text{A}\right)$ , then the probability of the complement is

  $P\left(\text{<mo>A</mo><mo>′</mo>}\right)=1-P\left(\text{A}\right)$

Calculation:

Event that “will happen” is the complement of event “that will not happen”.

Therefore we have to find the probability of event E.

  $\begin{array}{l}\therefore P\left(E\right)=1-P\left(E^{\prime }\right)\\ \Rightarrow P\left(E\right)=1-0.89\\ \Rightarrow P\left(E\right)=0.11\end{array}$

Hence the probability that the event will happen is 0.11.