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# Applied 40S March 3, 2009

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More on simulations and introduction to Pascal's Triangle.

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### Applied 40S March 3, 2009

1. 1. Multiple Guess, How Many Phone Numbers, and The Fundamental Principle of Counting Numbers by ﬂickr user Chaval Brasil
2. 2. Binomial Experiments & Probability Simulating Binomial Experiments: randBin(# of trials, prob. of success, # of simulations) What is the probability of getting exactly 2 heads when ﬂiping 3 coins 40 times? You'll need to know the the theoretical probability of this result is 3/8. Here is how to do the experiment on your calculator. Step Action 1. Press [Math] button on TI83 calculator. 2. Select [Prob]. 3. Select [randBin] (random binomial experiment). 4. Type in (1, 3/8, 40) . little predator 1 represents the outcome for success (failure is 0). 3/8 represents the theoretical probability of success. 40 represents number of times the experiment is repeated. 5. Press enter and a result will show in row. 6. Press [STO] [2nd] [L1] to store the results in List 1. 7. Press [2nd] [STAT]. 8. Select [MATH] [Sum] [2nd] [L1] to ﬁnd the sum of all the values in List 1. 9. Since quot;success = 1quot; and quot;failure = 0quot; this sum represents the number of successes. You can also use this website: Random.org http://www.random.org/
3. 3. Design an experiment using coins to simulate a 10 question true/ false test. What is the experimental probability of scoring at least HOMEWORK 70% on the test if you guess each answer?
4. 4. HOMEWORK Design an experiment to determine the probability of passing a six- question multiple choice test if you guess all the answers. Each question has four answers, and one answer is correct in each case. How many simulations would seem reasonable? What is the experimental probability of getting at least 50% on the test?
5. 5. Pascal's Triangle How many different patterns can you ﬁnd in the triangle?