# Designing Simulations

Warmup

Activity #1

Simulating Probability.

• Click the button.
• Click . Verify that the number of flips is equal to “# of heads” and “# of tails”.
• Match these numbers to the height of the bars in the graph. In a fair trial, the theoretical probabilities of having a tail or a head in a single throw of a coin is always 0.5.

(1.) From your result in the simulation, calculate the experimental probabilities of having a head

(2.) From your result in the simulation, calculate the experimental probabilities of having a tail.

Activity #2

`Simulate a Situation. `

• Read the story below and complete the activity.

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.

• If both coins land heads up, it represents a mouse with white fur.
• Any other result represents a mouse with brown fur.
• To simulate this situation, you can flip two coins at the same time for each baby mouse. If you don’t have coins, you can use this applet.
• Simulate a litter of 5 offsprings and record their results.
• Next, determine whether at least 2 of the offsprings have white fur. Record your results in the table below.

(1.) Based on your results, estimate the probability that the scientist’s experiment will be able to continue.

(2.) How could you improve your estimate?

(3.) For a certain pair of mice, the genetics show that each offspring has a probability of  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.

Challenge #1

Jada and Elena learned that 8% of students have asthma. They want to know the probability that in a team of 4 students, at least one of them has asthma. To simulate this, they put 25 slips of paper in a bag. Two of the slips say “asthma.” Next, they take four papers out of the bag and record whether at least one of them says “asthma.” They repeat this process 15 times.

• Jada says they could improve the accuracy of their simulation by using 100 slips of paper and marking 8 of them.
• Elena says they could improve the accuracy of their simulation by conducting 30 trials instead of 15.

(1.) Do you agree with either of them? Explain your reasoning.

(2.) Describe another method of simulating the same scenario.

Challenge #2

A rare and delicate plant will only produce flowers from 10% of the seeds planted. To see if it is worth planting 5 seeds to see any flowers, the situation is going to be simulated.

• Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds each and wait 6 months for the plants to grow and count the fraction of groups that produce flowers.
• Roll a standard number cube 5 times. Each time a 6 appears, it represents a plant producing flowers. Repeat this process 30 times and count the fraction of times at least one number 6 appears.
• Have a computer produce 5 random digits (0 through 9). If a 9 appears in the list of digits, it represents a plant producing flowers. Repeat this process 300 times and count the fraction of times at least one number 9 appears.
• Create a spinner with 10 equal sections and mark one of them “flowers.” Spin the spinner 5 times to represent the 5 seeds. Repeat this process 30 times and count the fraction of times that at least 1 “flower” was spun.

(1.) Which of these options is the best simulation?

(2.) For the others that you did not choose, explain why it is not a good simulation.

Quiz Time