Chapter 13.6, Problem 21PPS

(a)

To determine

To calculate: To find the probability of skateboarding being someone’s favorite sport

Answer to Problem 21PPS

The probability of skateboarding being someone’s favorite sport is $\frac{3}{8}$

Explanation of Solution

Given information: Graph showing the results of class survey about student’s favorite X Games sport

  

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

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

Calculation:

Graph is given as follows:

  

From the given graph,

Total number of students that are surveyed is calculated as follows:

  $\begin{array}{l}Total=8+6+4+15+7\\ Total=40\end{array}$

Also, number of students having favorite Games sport as Skateboarding $=15$

Now, probability of skateboarding being someone’s favorite sport is calculated as

  $\begin{array}{l}P=\frac{15}{40}\\ P=\frac{3}{8}\end{array}$

Conclusion:

Hence, required probability is $\frac{3}{8}$

(b)

To determine

To calculate: To find how many students will choose inline as their favorite sport

Answer to Problem 21PPS

  $120$ students will choose inline as their favorite sport

Explanation of Solution

Given information: Graph showing the results of class survey about student’s favorite X Games sport

  

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

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

Calculation:

Graph is given as follows:

  

From the given graph,

Total number of students that are surveyed is calculated as follows:

  $\begin{array}{l}Total=8+6+4+15+7\\ Total=40\end{array}$

Also, number of students having favorite Games sport as Inline skating $=6$

Now, probability of inline skating being someone’s favorite sport is calculated as

  $\begin{array}{l}P=\frac{6}{40}\\ P=\frac{3}{20}\end{array}$

Now, suppose number of students is $800$

Thus, number of students who will choose inline as their favorite sport is calculated as follows:

  $\begin{array}{l}Total=\frac{3}{20}\times 800\\ Total=3\times 40\\ Total=120\end{array}$

Conclusion:

Hence, $120$ students will choose inline as their favorite sport

(c)

To determine

To calculate: To find how many more students will prefer BMX than MotoX

Answer to Problem 21PPS

  $80$ morestudents will prefer BMX than MotoX

Explanation of Solution

Given information: Graph showing the results of class survey about student’s favorite X Games sport

  

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

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

Calculation:

Graph is given as follows:

  

From the given graph,

Total number of students that are surveyed is calculated as follows:

  $\begin{array}{l}Total=8+6+4+15+7\\ Total=40\end{array}$

Also, number of students having favorite Games sport as Inline skating $=8$

Now, probability of BMX being someone’s favorite sport is calculated as

  $\begin{array}{l}{P}_{BMX}=\frac{8}{40}\\ P_{BMX}=\frac{1}{5}\end{array}$

Now, suppose number of students is $800$

Thus, number of students who will choose BMX as their favorite sport is calculated as follows:

  $\begin{array}{l}{T}_{BTX}=\frac{1}{5}\times 800\\ T_{BTX}=160\end{array}$

Similarly, number of students having favorite Games sport as MotoX $=4$

Now, probability of MotoX being someone’s favorite sport is calculated as

  $\begin{array}{l}{P}_{MotoX}=\frac{4}{40}\\ P_{MotoX}=\frac{1}{10}\end{array}$

Now, suppose number of students is $800$

Thus, number of students who will choose MotoX as their favorite sport is calculated as follows:

  $\begin{array}{l}{T}_{MotoX}=\frac{1}{10}\times 800\\ T_{MotoX}=80\end{array}$

Hence, more number of students who will prefer BTX than MotoX is calculated as follows:

  $\begin{array}{l}More=T_{BTX}-T_{MotoX}\\ More=160-80\\ More=80\end{array}$

Conclusion:

Hence, $80$ more students will prefer BMX than MotoX