Chapter 10.3, Problem 5Q

To determine

To calculate:

The theoretical and experimental probability of die rolling a $5$ .

Answer to Problem 5Q

The theoretical probability of five coming up is $0.1667$ and the experiment probability is $0.2667$ .

Explanation of Solution

Given information:

Roll a six-sided die $30$ times.

  $5$ is rolled $8$ times.

Calculation:

First, the rolling of a six-sided dice, gives the theoretical probability of the face five coming up as,

  $\begin{array}{l}P\left(5co\min gup\right)\\ =\frac{1}{2}\\ =0.1667\end{array}$

Hence, the theoretical probability of five coming up is $0.1667$ .

Second, the experiment of throwing the dice for a $30$ times, gives the face five coming up for a number of $8$ times.

Hence, the depending on this trial, the experimental probability is thus.

  $\begin{array}{l}P\left(5co\min gup\right)\\ =\frac{8}{30}\\ =0.2667\end{array}$

Hence, the experiment probability is $0.2667$ .