3.6: Probabilities Through Simulations

1. CHS Statistics 3.6: Probabilities Through Simulations Objective: To simulate probabilities using random number tables and random number generators

2. Probabilities Through Simulations • Sometimes we are not sure our theoretical probability is correct. • To check we can conduct actual trials or collect real data to find probability value or verify that our theoretical results are correct. • Remember that the Law of Large Numbers tells us that the more trials were conduct, the closer our experimental probability will get to our theoretical probability. • We can also simulate the circumstances to learn how the results would occur in reality.

3. Simulation • A simulation of a procedure is a process that behaves the same way as trials of an experiment, so that similar results are produced. • To perform a simulation, you must assume that the “trials” are independent from one another.

4. Simulation Example: • When testing techniques of gender selection, medical researchers need to know probability values of different outcomes, such as the probability of getting at least 60 girls among 100 children. Assuming that male and female births are equally likely, describe a simulation that results in the genders of 100 newborn babies. • We could flip a coin 100 times and let Heads represent girls and tails represent boys, but who wants to do this?

5. Random Number Generators • Instead of flipping coins, we can use random number generators: • Random Digits Tables: These digit have been randomly generated. Recall its use from Chapter 1. • Graphing Calculator: Recall that we can use randInt in the graphing calculator. Go to Math  PRB  randInt( • Online Random Number Generators: There are many random number generators available online. • Random Number Generator Software: There are many software packages with random number generators. MiniTab is one of them. We will use this software later in the course.

6. Baby Example: • Let’s go back to the baby example: When testing techniques of gender selection, medical researchers need to know probability values of different outcomes, such as the probability of getting at least 60 girls among 100 children. Assuming that male and female births are equally likely, describe a simulation that results in the genders of 100 newborn babies. • Let’s practice using the random number table. • Since the chances of having a boy and a girl are equally likely, we want to consider the assignment of single digits 0-9: • How can we simulate this scenario in the calculator?

7. Dice Simulation: • Describe a procedure for simulating rolling two dice and finding the sums.

8. Free Throws: • Suppose a basketball player has an 80% free throw success rate. How can we use random numbers to simulate whether or not she makes a foul shot? How many shots might she be able to make in a row without missing?

9. Free Throws (Again): • How would our simulation procedure change if her success rate were only 72%?

10. Assignment AP Statistics- Chapter 11 Quiz