Question

E and F are mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E∣F).

Short answer

$P(EandF)=0$as E and F are mutually exclusive.

Step-by-step solution

Content Introduction

Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are events that are mutually exclusive. If two occurrences are considered discontinuous, the chances of both happening at the same time are nil.

Content Explanation

We are given: $P\left(E\right)=0.4andP\left(F\right)=0.5$

Also, it is given that E and F are exclusively mutual. Therefore, $P(EandF)=0$

Hence, it can be calculated as follow:

$$\begin{gathered} \mathrm{P}\left(\mathrm{E}\right|\mathrm{F})=\frac{\mathrm{P}(\mathrm{E}\mathrm{AND}\hspace{0.17em}\mathrm{F})}{\mathrm{P}\left(\mathrm{F}\right)} \\ \mathrm{P}(\mathrm{E}\left|\mathrm{F}\right)=\frac{0}{0.5} \\ \mathrm{P}\left(\mathrm{E}\right|\mathrm{F})=0 \end{gathered}$$