Lesson 10: Designing Simulations | Unit 8: Probability and Sampling

Multiple Select

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. Which of these options is the best simulation?

• Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds and wait 6 months for the plants to grow, then 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.

Open Ended

A rare and delicate plant will only produce flowers from 10% of the seeds planted. Explain why the following option is not a good simulation: Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds and wait 6 months for the plants to grow, then count the fraction of groups that produce flowers.

Open Ended

A rare and delicate plant will only produce flowers from 10% of the seeds planted. Explain why the following option is not a good simulation: 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.

Open Ended

A rare and delicate plant will only produce flowers from 10% of the seeds planted. Explain why the following option is not a good simulation: 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.

Open Ended

A rare and delicate plant will only produce flowers from 10% of the seeds planted. Explain why the following option is not a good simulation: 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.

Open Ended

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

Multiple Choice

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. Describe another method of simulating the same scenario.

• Use a random number generator to simulate the presence of asthma in students.
• Count the number of students with asthma in a classroom setting.
• Ask each student if they have asthma and record their answers.
• Use a deck of cards to represent students and draw four cards.

Multiple Choice

A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games. What is the probability that the team wins the series in exactly 5 games?

• 0.1250
• 0.2637
• 0.7500
• 0.5000

Multiple Choice

A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games. What counts as a successful outcome in your simulation?

• The team winning the series by winning 4 games.
• The opposing team winning the series by winning 4 games.
• The team winning 3 games in the series.
• The team losing the series by winning 4 games.

Multiple Choice

A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games. What is the estimated probability of the team winning the series?

• 0.8125
• 0.68359375
• 0.75
• 0.5