Question

Refer to the NASCAR and breakfast cereal example. What if the cereal company decided to make it harder to get some drivers’ cards than others? For instance, suppose the chance that each card appears in a box of the cereal is Jeff Gordon, $10\%$; Dale Earnhardt, Jr., $30\%$; Tony Stewart, $20\%$; Danica Patrick, $25\%$; and Jimmie Johnson,$15\%$. How would you modify the simulation in the example to estimate the chance that a fan would have to buy $23$ or more boxes to get the full set?

Short answer

Count the number of boxes that are required to sample to have at least $5$ boxes for each of the $5$ drivers.

Step-by-step solution

Step 1. Given Information

The percentages for assigning are $10\%,30\%,20\%,25\%$ and $15\%$ respectively.

Step 2. Concept

The probability of a single event occurring is calculated by dividing the number of events by the number of possible outcomes.

Step 3. Explanation

It is necessary to assign some integers ranging from $1$ to $100$, including $1-10$, $11-40,41-60,61-85,86-99,$ and $00$ Now, in Excel, use the random function to generate one drive for each of the five available drivers. Calculate or count the number of boxes that must be sampled in order to obtain at least $5$ boxes for each of the five drivers.