[math]\left(4.2+3\right)\div2[/math]
[math]\left(4.2+2.6+4\right)\div3[/math]
[math]\left(4.2+2.6+4+3.6\right)\div4[/math]
[math]\left(4.2+2.6+4+3.6+3.6\right)\div5[/math]
[size=150]A scientist is studying the genes that determine the color of a mouse’s fur. When two mice with brown fur breed, there is a 25% chance that each baby will have white fur. For the experiment to continue, the scientist needs at least 2 out of 5 baby mice to have white fur.[br][br][list][*]If both coins land heads up, it represents a mouse with white fur.[/*][*]Any other result represents a mouse with brown fur.[/*][/list][/size]
Based on the results from everyone in yout group, estimate the probability that the scientist’s experiment will be able to continue.
How could you improve your estimate?
For a certain pair of mice, the genetics show that each offspring has a probability of [math]\frac{1}{16}[/math] that they will be albino. Describe a simulation you could use that would estimate the probability that at least 2 of the 5 offspring are albino.
[b]Designing simulation #1:[/b] A man has 5 grandchildren, 4 girls and 1 boy. He thinks this is unusual. If the the probability that any child born will be a girl is [math]\frac{1}{2}[/math], what is the probability that a person who has 5 grandchildren will have exactly 4 granddaughters? Is this case unusual? Explain.[br][br][b]Designing simulation #2[/b]: To be on the safe side, three detectors were installed in a factory room to make sure that if there was a fire, at least one of them would signal a warning. The company that manufactured the smoke detectors indicated that, based on their testing, the probability that any one of the smoke detectors will work correctly is 0.75 (meaning that it works 75% of the time in the long run). This also means that there is a 25% chance that if there is smoke or a fire, the detector will not work! What is the probability[br]that if there was smoke in the factory, none of the 3 detectors would work? Does this probability[br]indicate a safety problem for the factory? Explain.[br][br][b]Designing simulation #3: [/b]An automobile factory has a reputation for assembling high quality cars. However, several new cars were shipped out to dealers that had a problem with the brakes. It is estimated that approximately 10% of the cars assembled at this factory have defective brakes. Five of these cars are shipped to a dealership near your school. What is the probability that none of the 5 cars will have defective brakes? Should the dealership be concerned? Explain.[br][br][b]Designing simulation #4: [/b]Your class is planning to collect data at a wildlife refuge center for the next 5 days. The staff at the refuge center indicated that there is a 40% chance of seeing an eagle during any one of the days of your visit. What is the probability that if your class visits the refuge for 5 days, you will see an eagle two or more days during your 5-day visit at the refuge center? Your teacher also indicated that if you[br]see 2 or more eagles during the 5 days, your class will be able to name one of the eagles as part of a[br]fundraiser. Do you think you have a good chance of being able to name an eagle? Explain.[br][br][b]Designing simulation #5[/b]: At a small animal emergency hospital, there is a 20% chance that an animal brought into the hospital may need to stay overnight. The hospital only has enough room to accommodate 2 animals per night. On a particular day, five animals were brought into the hospital. What is the probability that at least 3 of the animals may need to stay overnight? If seeing five animals per day is typical for this hospital, do you think the hospital is usually able to accommodate all of the animals that might have to stay[br]overnight? Explain.[br][br]Design a simulation that you could use to estimate a probability. Show your thinking. Organize it so it can be followed by others.
Explain how you used the simulation to answer the questions posed in the situation.