1. Unit 5 Lesson 6 Probability 6.7 Estimating Probabilities using Simulations

2. Simulation Simulation provides a means of estimating probabilities when we are unable to determine them analytically or it is impractical to estimate them by observation.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simulation Steps 1.Identify the event to be repeated. 2.Explain how you will simulate the trial.  Scheme (how many digits at a time?)  Stopping Rule  Ignore any repeats?  Outcome 3.Run several trials. 4.Analyze the outcomes. 5.State your conclusion (in the context of the problem, as always).

4. Suppose that couples who wanted children were to continue having children until a boy was born. Would this change the proportion of boys in the population? We will use simulation to estimate the proportion of boys in the population if couples were to continue having children until a boy was born. 1)We will use a single-random digit to represent a child, where odd digits represent a male birth and even digits represent a female birth. 2) Select random digits from a random digit table until a male is selected and record the number of boys and girls. 3) Repeat step 2 a large number of times.

5. Boy Simulation Continued... Below are four rows from the random digit table at the back of our textbook. Row 609387679956256584264 741010220475119479751 864736345123118004820 980287938404208912332 Trial 1: girl, boy Trial 2: boy Trial 3: girl, boy Trial 4: girl, boy Trial 5: boy Trial 6: boy Trial 7: boy Trial 8: girl, girl, boy Trial 9: girl, boy Trial 10: girl, girl, girl, girl, girl, girl, boy Continue this process a large number of times (at least 100 trials). Calculate the proportion of boys out of the number of children born. Notice that with only 10 trials, the proportion of boys is 10/22, which is close to 0.5!

6. Practice, Practice, Practice

7. Practice with Homework Handout Quiz C