7.SP.C.8. Find probabilities of Notes: Background Knowledge: compound events using organized Students use tree diagrams, frequency tables, and organized and lists, tables, tree diagrams, and simulations to determine the probability of compound events. simulation. (S) Probabilities are useful for predicting what will happen over the long a. Understand that, just as with simple run. Using theoretical probability, students predict frequencies of Lesson Ideas: events, the probability of a outcomes. Students recognize an appropriate design to conduct an Memory Games compound event is the fraction of experiment with simple probability events, understanding that the outcomes in the sample space for experimental data give realistic estimates of the probability of an which the compound event occurs. event but are affected by sample size. b. Represent sample spaces for compound events using methods Examples: such as organized lists, tables and Students conduct a bag pull experiment. A bag contains 5 marbles. tree diagrams. For an event There is one red marble, two blue marbles and two purple marbles. described in everyday language (e.g., Students will draw one marble without replacement and then draw double sixes”), identify the another. What is the sample space for this situation? Explain how you “rolling outcomes in the sample space which determined the sample space and how you will use it to find the compose the event. probability of drawing one blue marble followed by another blue c. Design and use a simulation to marble. generate frequencies for compound Suppose, over many years of records, a river generates a spring flood events. For example, use random about 40% of the time. Based on these records, what is the chance digits as a simulation tool to that it will flood for at least three years in a row sometime during the approximate the answer to the next five years? Illustrative Mathematics Tasks: question: If 40% of donors have type Show all possible arrangements of the letters in the word FRED using A blood, what is the probability that it a tree diagram. If each of the letters is on a tile and drawn at random, will take at least 4 donors to find one what is the probability that you will draw the letters F-R-E-D in that (a, b) with type A blood? order? What is the probability that your will have an F as the “word” first letter? Source: Arizona Academic Content Standards
7.SP.C.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (S) a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Notes: Students use tree diagrams, frequency tables, and organized and simulations to determine the probability of compound events. Probabilities are useful for predicting what will happen over the long run. Using theoretical probability, students predict frequencies of outcomes. Students recognize an appropriate design to conduct an experiment with simple probability events, understanding that the experimental data give realistic estimates of the probability of an event but are affected by sample size. Examples: Students conduct a bag pull experiment. A bag contains 5 marbles. There is one red marble, two blue marbles and two purple marbles. Students will draw one marble without replacement and then draw another. What is the sample space for this situation? Explain how you determined the sample space and how you will use it to find the probability of drawing one blue marble followed by another blue marble. Suppose, over many years of records, a river generates a spring flood about 40% of the time. Based on these records, what is the chance that it will flood for at least three years in a row sometime during the next five years? Show all possible arrangements of the letters in the word FRED using a tree diagram. If each of the letters is on a tile and drawn at random, what is the probability that you will draw the letters F-R-E-D in that order? What is the probability that your “word” will have an F as the first letter? Source: Arizona Academic Content Standards Background Knowledge: Lesson Ideas: Memory Games Illustrative Mathematics Tasks: (a, b)
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