Chapter 9.7, Problem 53E

To determine

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

Answer to Problem 53E

The probability that the event will not happen is $\frac{4}{5}$ .

Explanation of Solution

Given:

  $P\left(E\right)=\frac{1}{5}$

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.

  $\begin{array}{l}\therefore P\left(E^{\prime }\right)=1-P\left(E\right)\\ \Rightarrow P\left(E^{\prime }\right)=1-\frac{1}{5}\\ \Rightarrow P\left(E^{\prime }\right)=\frac{4}{5}\end{array}$

Hence the probability that the event will not happen is $\frac{4}{5}$ .