1. © 2010 Pearson Education, Inc. All rights reserved Chapter 9 9 Probability

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 2 NCTM Standard: Data Analysis and Probability  K–2: Children should discuss events related to their experience as likely or unlikely. (p. 400)  3–5: Children should be able to “describe events as likely or unlikely and discuss the degree of likelihood using words such as certain, equally likely, and impossible.” They should be able to “predict the probability of outcomes of simple experiments and test the predictions.” They should “understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.” (p. 400)

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 3 NCTM Standard: Data Analysis and Probability 6–8: Children should “understand and use appropriate terminology to describe complementary and mutually exclusive events.” They should be able “to make and test conjectures about the results of experiments and simulations.” They should be able to “compute probabilities of compound events using methods such as organized lists, tree diagrams, and area models.” (p. 401)

4. Slide 9.3- 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 9-3Using Simulations in Probability  A simulation is a technique used to act out a problem by conducting experiments whose outcomes are analogous to the original problem.   Using simulations, students typically estimate a probability using many trials rather than determine probabilities theoretically.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 5 Random Digits Table The digits in this table form a list of digits selected at random, often by a computer or a calculator.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 6 Random Digits Table To simulate a coin toss, pick a number at random to start, and then read across the table, letting an even digit represent “heads” and an odd digit represent “tails.”

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 7 A baseball player has a batting average of 0.400; that is, his probability of getting a hit on any particular time at bat is 0.400. Estimate the probability that he will get at least one hit in his next three times at bat. Example 9-10

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 8 Example 9-10 (continued) Use a random-digit table. A hit is represented by the digits 0, 1, 2, and 3. A 0, 1, 2, or 3 appears in 42 out of the 50 trials. An estimate for the probability is

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 9 To determine the number of fish in a certain pond, suppose we capture 300 fish, mark them, and throw them back into the pond. Suppose that the next day, 200 fish are caught and 20 of these are already marked. These 200 fish are then thrown back into the pond. Estimate how many fish are in the pond. Example 9-11

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 10 Because 20 of the 200 fish are marked, assume that of the fish in the pond are marked. Example 9-11 (continued) An estimate for the fish population of the pond is 3000.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 11 Example 9-12 Suppose Lucy makes enough batter for exactly 100 chocolate chip cookies and mixes 100 chocolate chips into the batter. If the chips are distributed at random and Charlie chooses a cookie at random from the 100 cookies, estimate the probability that it will contain exactly one chocolate chip. (Call this event E.)

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 12 Example 9-12 (continued) Construct a 10 x 10 grid to represent the 100 cookies Lucy made. Each square (cookie) can be associated with some ordered pair, where the first component is for the horizontal scale and the second is for the vertical scale. Use a random digit table (slide 9-60) to create ordered pairs, and then place a tally on the grid to represent each chip.

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 9.3- 13 Example 9-12 (continued) Estimate the probability that a cookie has exactly one chip by counting the number of squares with exactly one tally and dividing by 100.