1) Get 10 index cards or equal-sized pieces of paper. On each card put one of the digits, 0 through 9. (Put a different digit on each card, of course.) Throw the cards into a bag or a hat or some container where you can't see them. Mix them up. Pick a card, write down the digit, and then put the card back in the bag. Do this 100 times and you will have a nice sample for Fool the Teacher.
2) How many fives did you get in your sample?
3) Did you cheat when you made your sample for #1? If you are a little cheater, try to be very good at it. It might end up being more work. There are lots of different things I can check for (besides pairs of numbers).
4) On your Random Homework, I gave you a sample of 100 digits that contained no fives whatsoever. A random number generator (such as your index cards in a bag) might have produced such a sequence, but it's highly unlikely. Use the ideas behind a tree diagram to show just how unlikely that is. How often would I expect to see such a sequence? Do you think anybody in the class will walk in tomorrow and say that they got it? Or would you be very surprised to hear that?
5) Next compute the probability of seeing exactly one five. Remember to take into account all the different places in the sample where that five might have occurred.
6) Find the probability of seeing exactly two fives. Explain all aspects of your computation.
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