Chapter 10.7, Problem 1GP

To determine

To find: The experimental probability of rolling a $4$ then compare it with theoretical probability.

Answer to Problem 1GP

Experimental Probability: $P(4)=\frac{3}{15}=\frac{1}{5}$

Experimental probability is greater than the theoretical probability.

Explanation of Solution

Given information: A table containing numbers and corresponding frequencies.

Calculation:

Experimental Probability:

Adding the individual frequencies,

  $2+1+4+3+3+2=15$ , which is equal to the total number of rolls.

In experiment, $4$ came in $3$ rolls,

  $\Rightarrow P(4)=\frac{3}{15}=\frac{1}{5}$ or $20\%$ .

Theoretical Probability:

As there are $6$ different numbers, probability of getting $4$ uniquely is,

  $P(4)=\frac{1}{6}$ or about $16.67\%$ .

As $\frac{1}{6}<\frac{1}{5}$ , so $4$ came up more times than expected.

Thus, experimental probability is greater than the theoretical probability.