Coin tosses

Part I

If you toss 2 coins is the theoretical probability that you will get at least one tail 2/3? We are going to check out an excel spreadsheet that tosses 2 coins 100 times to evaluate the “empirical probability” of this outcome. In probability experiments there are two types of probabilities: theoretical vs empirical. Theoretical is what would happen in theory, so if we toss a coin we say that the probability of getting a tail is ½ since we assume both heads and tails are equally likely so there is a 1 in 2 chance of getting a tail. In actuality, we could toss a coin numerous times and end up getting all heads or 5 more heads than tails, or twice as many heads as tails, etc… What actually happens is called the empirical probability. So if I toss a coin 10 times and get 3 tails, I would say that the empirical probability of getting a tail is 3/10 but the theoretical probability is 5/10=1/2.

So back to our original question, if you toss 2 coins is the theoretical probability that you will get at least one tail 2/3? To evaluate this empirically, open up and save to your P-drive the excel spreadsheet Coin tosses and carry out the following:

To “run” the experiment of 100 tosses of 2 coins, just hit the F9 key.

1.  Run the experiment of tossing a coin 100 times 10 times and record how many times you received at least 1 tail and the empirical probability of getting at least 1 tail. (To “run” the experiment of 100 tosses of 2 coins, just hit the F9 key.)

2.  Look at the 10 values in #1 , is there a value that they all seem close to?

3.  Combine all of the 10 values from #1 and divide by 100x10, this will give you the empirical probability of getting at least 1 tail in 1000 tosses. How does this number compare to the value in #2?

4.  What do you think the theoretical probability of getting at least 1 tail in 2 tosses is? Explain.

Part II

1. In this activity you will look at the online applet: http://bcs.whfreeman.com/ips4e/cat_010/applets/Probability.html.

2. Run the applet 10 different times and record the relative frequency or empirical probability of tails and the following information for each trial:

  1. The number of sequences of 1 tail.
  2. The number of sequences of 2 tails
  3. The number of sequences of 3 tails
  4. The number of sequences of 4 tails
  5. The number of sequences of 5 tails
  6. The number of sequences of 6 tails
  7. The number of sequences of 7 tails
  8. The number of sequences of 8 tails

3.  Looking at your results in #2, what does it say about playing the lottery and using a number that has not showed up in awhile?

4.  Were you surprised about your results in #2?

5.  Do your results in #2 refute the fact that the theoretical probability of getting a tail is ½?