Chapter 13.6, Problem 16PPS

A.

To determine

The experimental probability of spinning a sum of $6$ .

Answer to Problem 16PPS

The experimental probability is $30\%$

Explanation of Solution

Given:

Sum	Frequency
$2$	$\left|\right|$
$3$	$\left|\right||$
$4$	$\left|\right|\left|\cancel{|}\right|\left|\right||$
$5$	$\left|\right|\left|\cancel{|}\right|$
$6$	$\left|\right|\left|\cancel{|}\right|\left|\right|\cancel{|}\left|\right||\cancel{|}$
$7$	$\left|\right|\left|\cancel{|}\right|\left|\right|$
$8$	$\left|\right|\left|\cancel{|}\right|\left|\right||$

Calculation:

Take, sum of $6$ occurrence and number of possible outcomes.

  $\begin{array}{l}=\frac{15}{2+3+8+6+15+8+8}\\ =\frac{15}{50}\\ =\frac{3}{10}\end{array}$

The probability which is experimental of spinning a sum of $6$ in this case is $\frac{3}{10}$ or $30\%$

Conclusion:

The experimental probability is $30\%$

B.

To determine

The experimental probability of spinning a sum of $8$ .

Answer to Problem 16PPS

The experimental probability is $16\%$

Explanation of Solution

Given:

Sum	Frequency
$2$	$\left|\right|$
$3$	$\left|\right||$
$4$	$\left|\right|\left|\cancel{|}\right|\left|\right||$
$5$	$\left|\right|\left|\cancel{|}\right|$
$6$	$\left|\right|\left|\cancel{|}\right|\left|\right|\cancel{|}\left|\right||\cancel{|}$
$7$	$\left|\right|\left|\cancel{|}\right|\left|\right|$
$8$	$\left|\right|\left|\cancel{|}\right|\left|\right||$

Calculation:

Now take the sum of $8$ occurrences and number of the possible outcomes.

  $\begin{array}{l}=\frac{8}{2+3+8+6+15+8+8}\\ =\frac{8}{50}\\ =\frac{4}{25}\end{array}$

The experimental probability of spinning a sum of $8$ in this case is $\frac{4}{25}$ or $16\%$

Conclusion:

The experimental probability is $16\%$

C.

To determine

The theoretical probability of spinning a sum of $8$ and compare it with experimental probability.

Answer to Problem 16PPS

The probability of spinning both spinners and having a sum of $8$ is $\frac{1}{16}$ or about $6\%$ .

Explanation of Solution

Given:

Sum	Frequency
$2$	$\left|\right|$
$3$	$\left|\right||$
$4$	$\left|\right|\left|\cancel{|}\right|\left|\right||$
$5$	$\left|\right|\left|\cancel{|}\right|$
$6$	$\left|\right|\left|\cancel{|}\right|\left|\right|\cancel{|}\left|\right||\cancel{|}$
$7$	$\left|\right|\left|\cancel{|}\right|\left|\right|$
$8$	$\left|\right|\left|\cancel{|}\right|\left|\right||$

Calculation:

The spinners are divided evenly into $4$ sections numbered one through four.

$\left(1,1\right)$	$\left(1,2\right)$	$\left(1,3\right)$	$\left(1,4\right)$
$\left(2,1\right)$	$\left(2,2\right)$	$\left(2,3\right)$	$\left(2,4\right)$
$\left(3,1\right)$	$\left(3,2\right)$	$\left(3,3\right)$	$\left(3,4\right)$
$\left(4,1\right)$	$\left(4,2\right)$	$\left(4,3\right)$	$\left(4,4\right)$

The sum of $8$ for the outcome $\left(4,4\right)$

So calculate the sum of $8$ and the total number of outcomes as,

  $\frac{1}{16}$

The probability of spinning both spinners and having a sum of $8$ is $\frac{1}{16}$ or about $6\%$ . The experimental probability of spinning a sum of $8$ is $16\%$ . So the sample answers is as the spinning a sum of $8$ in the experiment.

Conclusion:

The probability of spinning both spinners and having a sum of $8$ is $\frac{1}{16}$ or about $6\%$ .