Special Problem 5 – The Duck Hunters
Purpose: To plan, carryout, and analyze a probability simulation.
Group Size: Up to 4 Due: _____________
The Story: 10 Brothers love to duck hunt. Since they live out in the middle of nowhere, they had to become exceptional shooters, since it is a long way to town to get more ammunition.
Along the shoreline of their favorite lake, there are large bushes for them to hide in. So they usually spread themselves along the shoreline and lie in wait.
This one-day, they all spotted a group of 10 ducks on the water. The ducks swam into a patch of reeds, obscuring their chance to shoot them. So, they let loose their faithful dog, and he went over and made a big splash, startling all 10 ducks into flight. All 10 guns went off at once, and each shot hit a duck. However, since it was impossible for the Brothers to determine which ducks everyone was aiming at, it is very possible that some ducks did not get hit and flew away.
The question you must answer: On average, how many ducks would survive this situation?
There is no simple way to calculate this probability of survival with our formulas, so a simulation is necessary. In addition, you cannot simply start choosing digits from 0 – 9 and let that be the number of ducks that live. That would imply that all duck combinations are equally probable, which is clearly not the case.
So, you will first need to construct a simulation of the situation. Each time you do your simulation, you will count how many ducks survived. To get a good feel for the probability of survival, you will need to do the simulation A LOT of times. A couple hundred at least will be needed. While your calculator can do this, I would recommend doing it on Excel. Once you construct the simulation, your teacher can help you set up the spreadsheet.
Your report will have the usual cover sheet, then a simple paragraph on what the paper is about along with a description of the simulation. A frequency table showing the distribution of survival, and either a dot plot or histogram will follow this. Comment on the shape, center, and spread of your graph.
Use your results to answer these three questions:
1. What is the probability that exactly 3 ducks survive?
2. What is the probability that at most 4 ducks survive?
3. What is the probability that at least 6 ducks survive?
Finally, answer the original question: On average, how many ducks would survive?
Grade breakdown: All elements present: 10% Simulation plan 15%
Data/graph/analysis 20% Probability answers 20%
