Chapter 13.6, Problem 6CYU

To determine

To calculate: To find the experimental probability of rolling a $4$ and then compare it to the theoretical probability

Answer to Problem 6CYU

Experimental probability of rolling a $4$ is $0.2$ and is more than the theoretical probability of rolling a $4$

Explanation of Solution

Given information: Table showing the results of an experiment in which a die was rolled

Number	Frequency
1	II
2	I
3	IIII
4	III
5	III
6	II

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

  $\mathrm{Probability}=\frac{Event}{Outcomes}$

Calculation:

Results of experiments are given as follows:

Number	Frequency
1	II
2	I
3	IIII
4	III
5	III
6	II

From above table, total frequency $=2+1+4+3+3+2=15$

Frequency of $4$ $=3$

Thus, experimental probability of rolling a $4$ is calculated as

  $\begin{array}{l}{P}_E=\frac{3}{15}\\ P_E=\frac{1}{5}\\ P_E=0.2\end{array}$

Also, theoretical probability of rolling a $4$ is calculated as

  $\begin{array}{l}{P}_T=\frac{1}{6}\\ P_T=0.167\end{array}$

On comparing, experimental probability of rolling a $4$ is more than the theoretical probability

Conclusion:

Hence, experimental probability of rolling a $4$ is $0.2$ and is more than the theoretical probability of rolling a $4$