Chapter 10.2, Problem 25E

(a)

To determine

To find: theprobability that you are chosen “fair” means equally likely.

Answer to Problem 25E

The correct answer is: 0.05.

Explanation of Solution

Given:

There are 20 candidates

The person worked for 4 hours

The group of 19 students worked for 45 hours.

Calculation:

Since, fair means equally likely, therefore, the best way to select a candidate is to make 20 equal chits and write a code number inside it corresponding to each volunteer. Then draw a chit at random from the 20 chits. Assume, event A denote choosing the concerned volunteer. Therequired probability is as follows:

  $\begin{array}{l}P\left(A\right)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\\ =\frac{1}{20}\\ =0.05\end{array}$

Conclusion:

Therefore, the correct answer is: 0.05.

(b)

To determine

To find: the probability that you are chosen “fair” means proportional to the number of hours each student worked in preparation.

Answer to Problem 25E

The correct answer is: 0.089.

Explanation of Solution

Calculation:

Since, fair means proportional to the number of hours each student worked, therefore, the best way to select a candidate is to make 45 equal chits and write the number of hours each student worked inside it. Then draw a chit at random from the 45 chits. Assume, event B denote choosing the concerned volunteer. The required probability is as follows:

  $\begin{array}{l}P\left(A\right)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\\ =\frac{4}{45}\\ =0.089\end{array}$

Conclusion:

Therefore, the correct answer is: 0.089.