Chapter 9.7, Problem 51E

To determine

To find the probability of the event that will not happen.

Answer to Problem 51E

The probability that the event will not happen is 0.27

Explanation of Solution

Given:

  $P\left(E\right)=0.73$

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

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

Calculation:

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

Therefore we have to find the probability of complement of event E.

  $\begin{array}{l}\therefore P\left(E^{\prime }\right)=1-P\left(E\right)\\ \Rightarrow P\left(E^{\prime }\right)=1-0.73\\ \Rightarrow P\left(E^{\prime }\right)=0.27\end{array}$

Hence the probability that the event will not happen is 0.27