1
Thank you downloading this Probability Lab. I would greatly appreciate your feedback on my blog and/or on my Teachers Pay Teachers Account. Be sure to read my terms of use below. Sincerely, Darci the STEM Mom http://www.STEMmom.org All downloads are copyright protected. Please feel free to use these downloads for your own personal family and classroom use. You are welcome to: •
•
•
•
Save the files to your computer and print off copies for yourself or classroom whenever you would like Comment on the lesson publically; online or in presentations, but please mention and link directly to my website (http://www.STEMmom.org) Write blog posts (or post photos on a school website) that include photos of your students using my files as long as proper credit is given to Darci the STEM Mom, with a link back to post where the STEMmom.org lesson is described. Post the electronic version of the lesson online ONLY if: o It is for student/parent access AND o It is password protected (not accessible by the general public) You may not: •
•
•
Post the electronic version of the lesson online with the intent to share it with other teachers, educators, and administrators. Host any of my files as your own Sell any of my files 2
Name ______________________________________________________ Science Course_____________________________________ Pre Lab Due _____________________________ Post Lab Due ___________________________ Grade _____________________ Probability Lab Background Probability is the likelihood that a particular event will happen. Math people think of probability as a number than describes the odds of a particular thing happening. While this may not seem very exciting, probability is important in many different jobs. For example, in biology, scientists that study genetics can calculate the likelihood that the children of a couple will have a genetic disorder. Another example would be in stores, when marketing, researchers calculate the probability of where consumers are more likely to look on the shelves so higher priced products can be placed where most people look. Calculating Probability Calculations Examples Expected Results: On a spinner numbered 1-­‐6 the chance you # possible = x 100 = _______ % have of landing on the # 4 can be calculated by: Total # 1/6 * 100 = 16% Observed Results: On a spinner numbered 1-­‐6, we performed 50 # Observed_____________ x 100 = _______ % trials to see how often we landed on the # 4; which was 9 times. Total Number possible 9/50 * 100 = 18% PreLab Questions 1. When flipping a single coin, calculate the probability that it will land with the “heads” side up. Show your work. 2. What is the probability that a single coin will land with the “tails” side up? Show your work. When flipping two coins at the same time, you have four different ways the coins can land; Heads/Heads, Tails/Tails, or Heads/Tails, or Tails/Heads. 3. When flipping two coins, calculate the probability that the coins will land with the both heads. Show your work. 3
4. What is the probability that the 2 coins will both land on tails? Show your work. 5. What is the probability that the 2 coins will land with the first coin heads up and the second showing tails? Show your work. 6. What is the probability that the 2 coins will land with the first coin tails and the second heads? Show your work. These supplies are needed 2 coins 1 cup Procedure for Part 1 Put ONE coin in a cup, cover it with your hand, and shake the cup. You can either let the coin fall onto the table or simply look into the cup to determine whether it landed head side up or tails side up. Make a tally mark for either heads or tails in the table below. After each 10 flips, work out the percentage of heads and tails and see how far it is from the expected outcome. Part One: One Coin Flip Data Table Heads Percentage Flips 1-­‐10 Flips 11-­‐20 Tails Percentage Totals 1-­‐20 ______________/20 x 100 = ______________/20 x 100 = Flips 21-­‐30 ______________/30 x 100 = Flips 31-­‐40 ______________/30 x 100 = Totals 1-­‐40 ______________/40 x 100 = ______________/40 x 100 = Flips 41-­‐50 Totals 1-­‐50 ______________/50 x 100 = ______________/50 x 100 = Class Totals _____________/__________ x 100 ____________/__________ x 100 Totals 1-­‐30 = = 4
Procedure for Part 2 Now you’ll need a second cup. Place one coin into each cup and shake them. For this part of the lab it is important that you keep track of which coin came from which cup. This matters because we are recording heads/tails, AND tails/heads. Place a tally mark in the appropriate data table below. Do this 50 times. After each ten flips, work out the percentage of 2 heads, 1 head/1tail and 2 tails and see how far it is from the expected outcome. Part Two: Two Coin Flip Data Table 2 heads % head/tails % tails/heads % 2 tails % Flips 1-­‐10 Flips 11-­‐20 Totals 1-­‐20 Flips 21-­‐30 Totals 1-­‐30 Flips 31-­‐40 Totals 1-­‐40 Flips 41-­‐50 Totals 1-­‐50 Class Total Post Lab Questions 1. Fill out the data table below to help you better compare the results. Using the calculations you made in the prelab questions, fill in the “Expected Outcome” in both the one-­‐coin toss and the two-­‐coin toss table below. Then fill in the column labeled, “My Data (1-­‐50)” with your final calculations, raw data (total number) and percent. Then in the last column, fill in the calculations from the class’ data. Table Comparing Results from the 1 coin toss Expected Outcome My Data (1-­‐50) Class Data heads tails 5
Table Comparing Results from the 2 coin toss Expected Outcome My Data (1-­‐50) Class Data heads/heads heads/tails tails/heads tails/tails 2. Statistically, how should our data percentages compare to the expected outcome percentages as the number of flips increase? Looking back at your data tables showing all of your flips, did you find this true? Explain. 3. How do the results in the “My Data” column compare to the expected outcome? Do you have any explanations for the differences or similarities? 4. How do the results in the “Class Data” column compare to the expected outcome? Do you have any explanations for the differences or similarities? 5. Describe several different techniques you observed while people were flipping their coins. Do you think this difference impacted the outcome of the trials? Explain why. 6. Apply what you’ve learned: Let’s say in the news you heard that some researchers announced that there may be a link between a new artificial sweetener and cancer in rats. How confident in their results would you be if you knew they studied 15 rats? Would your view of the research change if you knew they studied 8000 rats? Explain your thinking. References SOS (Switched on Schoolhouse): Probability Lab from Biology Course. 2011. Kleczek, Jana. (Jan 18, 2010) Biology Coin Probability. Accessed online http://www.slideshare.net/jkleczek/biology-­‐coin-­‐probability on Jan. 10, 2012. 6
Teachers’ Answer Key Probability Lab Background Probability is the likelihood that a particular event will happen. Math people think of probability as a number than describes the odds of a particular thing happening. While this may not seem very exciting, probability is important in many different jobs. For example, in biology, scientists that study genetics can calculate the likelihood that the children of a couple will have a genetic disorder. Another example would be in stores, when marketing, researchers calculate the probability of where consumers are more likely to look on the shelves so higher priced products can be placed where most people look. Calculating Probability Calculations Examples Expected Results: On a spinner numbered 1-­‐6 the chance you # possible = x 100 = _______ % have of landing on the # 4 can be calculated by: Total # 1/6 * 100 = 16% Observed Results: On a spinner numbered 1-­‐6, we performed 50 # Observed_____________ x 100 = _______ % trials to see how often we landed on the # 4; which was 9 times. Total Number possible 9/50 * 100 = 18% PreLab Questions 1. When flipping a single coin, calculate the probability that it will land with the “heads” side up. Show your work. 1/2 * 100 = 50% 2. What is the probability that a single coin will land with the “tails” side up? Show your work. 1/2 * 100 = 50% When flipping two coins at the same time, you have four different ways the coins can land; Heads/Heads, Tails/Tails, or Heads/Tails, or Tails/Heads. 3. When flipping two coins, calculate the probability that the coins will land with the both heads. Show your work. 1/4 * 100 = 25% (The denominator is 4 because there are 4 total outcomes that are possible) 7
4. What is the probability that the 2 coins will both land on tails? Show your work. 1/4 * 100 = 25% 5. What is the probability that the 2 coins will land with the first coin heads up and the second showing tails? Show your work. 1/4 * 100 = 25% (If you want you could lump H/T and T/H into the same category, and it would be 2/4 *100 = 50%.)
6. What is the probability that the 2 coins will land with the first coin tails and the second heads? Show your work. 1/4 * 100 = 25% These supplies are needed 2 coins 1 cup Procedure for Part 1 Put ONE coin in a cup, cover it with your hand, and shake the cup. You can either let the coin fall onto the table or simply look into the cup to determine whether it landed head side up or tails side up. Make a tally mark for either heads or tails in the table below. After each 10 flips, work out the percentage of heads and tails and see how far it is from the expected outcome. Part One: One Coin Flip Data Table Answers Will Vary, but be sure that students are adding the totals of the white rows into the gray ones. Heads Percentage Flips 1-­‐10 Flips 11-­‐20 Tails Percentage Totals 1-­‐20 ______________/20 x 100 = ______________/20 x 100 = Flips 21-­‐30 ______________/30 x 100 = Flips 31-­‐40 ______________/30 x 100 = Totals 1-­‐40 ______________/40 x 100 = ______________/40 x 100 = Flips 41-­‐50 Totals 1-­‐50 ______________/50 x 100 = ______________/50 x 100 = Class Totals _____________/__________ x 100 ____________/__________ x 100 Totals 1-­‐30 = = 8
Procedure for Part 2 Now you’ll need a second cup. Place one coin into each cup and shake them. For this part of the lab it is important that you keep track of which coin came from which cup. This matters because we are recording heads/tails, AND tails/heads. Place a tally mark in the appropriate data table below. Do this 50 times. After each ten flips, work out the percentage of 2 heads, 1 head/1tail and 2 tails and see how far it is from the expected outcome. Part Two: Two Coin Flip Data Table Answers Will Vary, but be sure that students are adding the totals of the white rows into the gray ones. 2 heads % head/tails % tails/heads % 2 tails % Flips 1-­‐10 Flips 11-­‐20 Totals 1-­‐20 Flips 21-­‐30 Totals 1-­‐30 Flips 31-­‐40 Totals 1-­‐40 Flips 41-­‐50 Totals 1-­‐50 Class Total Post Lab Questions 7. Fill out the data table below to help you better compare the results. Using the calculations you made in the prelab questions, fill in the “Expected Outcome” in both the one-­‐coin toss and the two-­‐coin toss table below. Then fill in the column labeled, “My Data (1-­‐50)” with your final calculations, raw data (total number) and percent. Then in the last column, fill in the calculations from the class’ data. Table Comparing Results from the 1 coin toss Answers will vary for last 2 columns. Expected Outcome My Data (1-­‐50) Class Data heads 50% tails 50% 9
Table Comparing Results from the 2 coin toss Answers will vary for last 2 columns. Expected Outcome My Data (1-­‐50) Class Data heads/heads 25% heads/tails 25% tails/heads 25% tails/tails 25% 8. Statistically, how should our data percentages compare to the expected outcome percentages as the number of flips increase? Looking back at your data tables showing all of your flips, did you find this true? Explain. As the number of flips increase, our percentages should move closer and closer to the expected outcome. Students should look back at their data and see whether or not that happened with their numbers. For some it will be, and for other it won’t. 9. How do the results in the “My Data” column compare to the expected outcome? Do you have any explanations for the differences or similarities? Students should comment on how their data compare to the expected. Explanations might include varying of techniques, or their low number of trials. 10. How do the results in the “Class Data” column compare to the expected outcome? Do you have any explanations for the differences or similarities? Depending on your class size, the numbers are most likely closer to the expected outcome compared to their own data. 11. Describe several different techniques you observed while people were flipping their coins. Do you think this difference impacted the outcome of the trials? Explain why. Answers will vary. Most likely technique didn’t impact results, unless they were only flipping the coin front to back watching to make sure they got “good” numbers. 12. Apply what you’ve learned: Let’s say in the news you heard that some researchers announced that there may be a link between a new artificial sweetener and cancer in rats. How confident in their results would you be if you knew they studied 15 rats? Would your view of the research change if you knew they studied 8000 rats? Explain your thinking. With only 15 rats, one can’t be certain that the connection between the sweetener and cancer isn’t because of other issues. But if the study used 8000 rats, you can be more confident that there is a link between the two. References SOS (Switched on Schoolhouse): Probability Lab from Biology Course. 2011. Kleczek, Jana. (Jan 18, 2010) Biology Coin Probability. Accessed online http://www.slideshare.net/jkleczek/biology-­‐coin-­‐probability on Jan. 10, 2012.