Math Forum - Problem of the Week


Heads and Tails

  1. How many times would you have to flip a coin in order to guarantee at least one head and one tail?
  2. How many times would you have to flip a coin in order to be "pretty sure" that you'd get at least one head and one tail... is one flip enough? Two? Twenty?
  3. If you had a stack of 500 Pokemon cards, with 250 Pikachu and 250 Bulbasaur cards, would you expect to have to draw more, fewer, or about the same number as your answer to Question 2, to get a complete set? Explain.

To start answering Question 2, run at least 10 trials, flipping a coin (and counting the number of flips) until you get a head and a tail. For example, you might get T-T-T-H, for a count of 4 flips, in one trial. Based on your results, see if you can give an answer to the question "How many times would you have to flip a coin in order to be 'pretty sure' that you'd get at least one head and one tail." How confident are you of your answer? Explain how you used the results of your 10 trials to answer the question.

To get a better answer to Question 2, open this math tool: Cereal Box Problem. The situation can be simulated by choosing 2 prizes. Click the "Log trials" box (a small java window will open). Run a few dozen trials to try to answer the question. How confident are you of your answer? Did you use the same process for obtaining an answer as when you tossed a coin by hand?

Another math tool that simulates flipping coins is Random.org/coins. Select the number of coins you think you'll need to be "pretty sure" you'll get heads and tails, and choose what type of coin you want to flip. Then you can repeat the trials as much as you want, though you'll have to keep track of the results by hand.

When you submit your answers, be sure to explain your reasoning.


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