Chapter 9.7, Problem 3E

To determine

To fill the blank in the statement “The formula for the _____ of an event is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ , where $n\left(E\right)$ is the number of equally likely outcomes in the event and $n\left(S\right)$ is the number of equally likely outcomes in the sample space.”

Answer to Problem 3E

The formula for the probability of an event is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ , where $n\left(E\right)$ is the number of equally likely outcomes in the event and $n\left(S\right)$ is the number of equally likely outcomes in the sample space.

Explanation of Solution

Given:

The formula for the _____ of an event is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ , where $n\left(E\right)$ is the number of equally likely outcomes in the event and $n\left(S\right)$ is the number of equally likely outcomes in the sample space.

If an event E has $n\left(E\right)$ equally likely outcomes and its sample space S has $n\left(S\right)$ equally likely outcomes, then the probability of event E is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ .

Therefore,

The formula for the probability of an event is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ , where $n\left(E\right)$ is the number of equally likely outcomes in the event and $n\left(S\right)$ is the number of equally likely outcomes in the sample space.