# Common Core Standards: Math

### Statistics and Probability 7.SP.C.8.c

8c. 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?

Your students thought they were getting out of doing too much critical thinking? They thought they could coast along with simple plugging and chugging? Insert maniacal laugh here.

This sub-standard isn't about representing sample spaces or calculating theoretical probabilities; it's about having students understand a compound probability situation so well that they can develop a simulation for it. In other words, they should be able to come up with a compound probability situation that shares the exact same sample space with a given situation. Students can then run that simulation in order to calculate probabilities.

Take this scenario, for instance: A cereal company put one toy in the each box of cereal. The toys come in red, yellow, green, or blue. What is the probability that someone will need to buy at least four boxes of cereal until they get a blue toy?

Using formulas for the probabilities of compound events, the problem would be challenging for most high school students. But luckily for seventh graders, they aren't bogged down by difficult formulas or number crunching; they should be able to to simulate this experiment in order to find the probability they're interested in.

An easy simulation would be for each student to get four small, equal-sized pieces of paper, write one of the four colors on each of the pieces of paper, and place the paper in a bowl. The students could then begin the experiment by randomly choosing pieces of paper until one of them says BLUE, always making sure to return any paper they draw back into the bowl. After running this simulation enough times, students should have a table that looks something like this.

 Number of Tries Until BLUE Was Chosen Frequency 1 50 2 38 3 28 4 21 5 16 6 13 7 10 8 8 9 6 10 4 11 3 12 2

Since the question asked the students to find the probability that someone will need to buy at least four boxes (read: four or more boxes) of cereal until they get a blue toy, the students would add up all the frequencies from 4 tries until 12 tries and divide this sum by the total number of trials done. Using this data, they can conclude that the probability is about 0.4.