Question

If the probability that an event will happen is $0.2$, what is the probability of the event's complement?

Answer 1

Find the probability of the event's complement.

Given that,

The probability is $\mathrm{P}\left(\mathrm{A}\right)=0.2$.

Use the event's complement formula $\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}(\mathrm{A}\text{'})=1$.

Here, $\mathrm{P}\left(\mathrm{A}\right)$ is the event probability and $\mathrm{P}(\mathrm{A}\text{'})$ is the complement of event probability.

Modify the formula to get the event's complement:

$\Rightarrow \mathrm{P}(\mathrm{A}\text{'})=1-\mathrm{P}\left(\mathrm{A}\right)$.

Substitute the value $\mathrm{P}\left(\mathrm{A}\right)=0.2$ in the above formula:

$\begin{array}{rcl}& \Rightarrow & \mathrm{P}(\mathrm{A}\text{'})=1-0.2\\ & =& 0.8\end{array}$

Hence, the probability of the event's complement whose event probability $\mathbf{0}\mathbf{.}\mathbf{2}$ is $\mathbf{0}\mathbf{.}\mathbf{8}$.