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The dog ate my homework!

Analyze chances of wrongful accusations in class experiment with die rolls by Mr. L. I. Detector. Record results, compare, and calculate probabilities to understand outcomes fully.

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The dog ate my homework!

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  1. The dog ate my homework! A certain teacher, Mr L I Detector, claims he can tell when students are lying about their homework. This is true. Unfortunately, he also accuses some students who are telling the truth. So what are the chances that someone will be wrongly accused?

  2. In your pairs you should have: • a die • recording grid • red, blue, green and yellow coloured pencils • a worksheet

  3. How it works: Throw the die once to determine whether the student is lying or telling the truth. 6 means they are lying. If they are lying, they will be accused. If they are telling the truth, throw the die a second time to see whether or no they will be accused. 1 means they are accused. Telling the truth lying accused Not accused

  4. Throw the die Student is lying. Colour top box red. Student is telling the truth. Colour top box blue. Throw dice again Mr D knows student is lying. Accuses student. Colour bottom box yellow. Mr D accuses the student Colour bottom box yellow. Mr D believes the student Colour bottom box green.

  5. What do each of these mean? Why can't you have red and green? Now repeat the experiment 36 times in total and record on your sheet   You should end up with 36 pairs of coloured blocks.

  6. Throw the die Student is lying. Colour top box red. Student is telling the truth. Colour top box blue. Throw dice again Mr D knows student is lying. Accuses student. Colour bottom box yellow. Mr D accuses the student Colour bottom box yellow. Mr D believes the student Colour bottom box green.

  7. So what are the chances that someone will be wrongly accused? What does the evidence on your recording sheet suggest? Are you surprised by what you see? Complete the tree diagram and 2-way table for the results of your experiment. Complete the tree diagram and 2-way table for what you would EXPECT to happen. How do your results compare?

  8. How do the experimental results compare with what we would expect? • How many students in total are accused? Are you surprised?  Why (not)? • How many innocent students are accused? • What proportion of innocent students are accused? • So what is the probability that a truthful student is accused? 

  9. How many accused students are telling the truth? What proportion of accused students are telling the truth? Is the probability that a truthful student is accused the same as the probability that an accused student is telling the truth? Are you surprised? Why (not)?

  10. Which figures are in both the tree diagram and the 2-way table, which are not? What are the advantages of the tree diagram? How about the 2-way table? What information can you find easily from each, what is more difficult or impossible to find?

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