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Name_____________________________________ Class____________________________ Date________________ Lesson 12-1 Probability Distributions Lesson Objectives 1 Making a probability distribution 2 Using a probability distribution in conducting a simulation NAEP 2005 Strand: Data Analysis and Probability Topic: Probability Local Standards: ____________________________________ Vocabulary. All rights reserved. A frequency table is Cumulative probability is A probability distribution is Example. 1 Finding Probability Use the frequency table. Find the probability that a student is involved in at least one extra-curricular activity. © Pearson Education, Inc., publishing as Pearson Prentice Hall. P (more than one activity) P (one activity) 720 720 720 720 720 Find the experimental probability for each event in the table that represents at least one extra-curricular activity. More than one activity 144 One activity 360 No activities 216 Total Students 720 Add to find the cumulative probability. Quick Check. 1. Use the information in Example 1. Find the probability that a student is involved in one activity or no activities. Daily Notetaking Guide Algebra 2 Lesson 12-1 231 Name_____________________________________ Class____________________________ Date ________________ Example. 2 Probability Distributions Suppose you spin two spinners. Each spinner has 4 possible outcomes: 1, 2, 3, and 4. Show the probability distribution for the sum of the numbers. Method 1 Make a frequency table. Extend the table to include probabilities. Spinning Two Spinners 3 2 Sum 4 5 6 7 8 Frequency There are 16 possible outcomes. Divide to find the probability. 16 16 16 16 16 16 16 All rights reserved. Probability Method 2 Graph. Spinning Two Spinners 3 16 1 16 2 3 4 5 6 7 8 2. Use a table or a graph to show the probability distribution for the roll of one number cube labeled with numbers 1–6. 232 Algebra 2 Lesson 12-1 Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. Quick Check. Name_____________________________________ Class____________________________ Date ________________ Example. 3 Genetics Use the information in the chart. Graph the probability distribution for each sample space. Inherited Gene Pairs From One Recessive and One Hybrid Pea Plant Parent Plant All rights reserved. Parent Plant r r R Rr Rr r rr rr RR dominant gene pair (red flower) Rr hybrid gene pair (pink flower) rr recessive gene pair (white flower) © Pearson Education, Inc., publishing as Pearson Prentice Hall. 3 4 2 4 1 4 Plant Color Distribution {red, pink, white} 1 Probability Probability Genotype Distribution {RR, Rr, rr} 1 RR Rr rr Event 3 4 2 4 1 4 Red Pink White Event Quick Check. 3. Make a probability distribution table for each sample space in Example 3. Daily Notetaking Guide Algebra 2 Lesson 12-1 233 Name_____________________________________ Class____________________________ Date ________________ Example. 4 Market Research The probability of an information desk at a library receiving C calls each hour varies according to the following distribution. C 0 1 2 3 4 5 P(C) 0.05 0.15 0.25 0.3 0.2 0.05 Outcome Probability Cumulative Probability 0 0.05 0.05 1 0.15 0.20 2 0.25 3 0.30 0.20 5 0.05 01 – 05 Since P(0) 0.05, assign numbers to this outcome. 75 There are – – 0.75 46 – – 1.00 numbers from 46 to 75. 96 – 100 Step 2 Conduct the simulation. Model an eight-hour period by generating eight random numbers from 1 to 100. Hour 1st 2nd 3rd 4th 5th 6th 7th 8th Random 95 91 15 52 41 74 5 34 numbers Number of calls 4 4 Step 3 Interpret the simulation. A total of 3 0 calls came in over an eight-hour period. Quick Check. 4. Use the information in Example 4. Conduct a simulation to predict the number of calls received during a 16-hour period. 234 Algebra 2 Lesson 12-1 Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. 4 Assigned Numbers All rights reserved. Use random numbers to predict the number of calls received during an eight-hour shift. Step 1 Set up a random-number simulation. Assign numbers from 1 to 100 based on the probability of each event. Use cumulative probabilities.