Chapter 11.5, Problem 10PPSE

Solution

To state: The number of times a customer have to spend over $50 in order to get all 3 different discount offers if a grocery store is giving away scratch-off tickets to each customers when they spend over $50 and there are three different discount offers randomly and equally distributed among scratch-off tickets.

A person needs to spend $50 nine times to get three different discount offers.

Given information:

A coach wants to select 5 of his 16 players at random to help with a youth basketball camp this weekend. He assigns a two-digit number from 01 to16 to each player.

Explanation:

Simulation is a technique that is used to act out a problem by conducting experiments and its outcomes are analogous to the original problem.

Students can estimates a probability using many trails rather than determine probabilities theoretically while using simulation.

Choose a number between 1 and 9. Draw a random number; the first discount offer is represented by the number between 1, 2, and 3; the second discount offer is represented by the number 4, 5; and the third discount offer is represented by the number 7, 8.

Each number has an equal chance of being selected. The result of the first trial is shown below:

  

The result shows that a person has to spend $4+1+3=8$ times over $50 to get three different discount offers.

Now repeat the simulation several times.

Let’s conduct the simulation 24 more times and the result will indicate that a person can expect to spend $50 following number to get three different discount offers:

  $\begin{array}{l}91275156781011136\\ 98129131012711865\end{array}$

The number of spend over $50 to get three different discount offers is:

  $\begin{array}{c}\text{Average}=\frac{\begin{array}{l}9+12+7+5+15+6+7+8+10+11+13+6+\\ 9+8+12+9+13+10+12+7+11+8+6+5\end{array}}{25}\\ =\frac{227}{25}\\ =9.08\end{array}$

Therefore, on an average, a person needs to spend $50 nine times to get three different discount offers.