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# Slides February 23rd

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### Slides February 23rd

1. 1. Experimental and Theoretical Probability In a family of three children, what is the probability that 2 of the children will be girls? one two three
2. 2. In a family of three children, what is the probability that 2 of the children will be girls? Experimental Probability: The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played.
3. 3. In a family of three children, what is the probability that 2 of the children will be girls? Theoretical Probability: The chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4. Contrast this with experimental probability.
4. 4. In a family of three children, what is the probability that 2 of the children will be girls? Theoretical Probability
5. 5. Binomial Experiments & Probability Simulating Binomial Experimets: 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) . 1 represents the outcome for success (failure is 0). little predator 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. http://www.random.org/ You can also use this website: Random.org
6. 6. HOMEWORK What is the probability of spinning each of the following using the spinner shown? The colours on the spinner are red, yellow, and blue. 1. P(red) 2. P(yellow) 3. P(green) 4. P(red, yellow or blue) 5. P(not red)
7. 7. HOMEWORK Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring at least 70% on the test if you guess each answer?
8. 8. 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?