Sanderson M. Smith
Home  About Sanderson Smith  Writings and Reflections  Algebra 2  AP Statistics  Statistics/Finance  Forum
The questions below appeared on the AP Statistics ListServe. They represents a very common misconception about probability, and, in this particular case, coinflipping.
Response: It is true that if you flip a coin many, many times, the proportion of heads and the proportion of tails should both approach 50%. Note, however, that the writer is talking about differences, not proportions. I'll illustrate below with madeup numbers. (I didn't do a simulation.) Note that the difference between heads and tails continues to get larger, but the respective proportions approach 50%.



# (HEADSTAILS) 
PROP. HEADS 
PROP. TAILS 


















Somewhat related to the above: A few years ago, a parent of one of my students asked me this question.
Note that the questionasker is thinking that the difference between number of heads and number of tails should approach zero after many flips. I know that the parent who asked the question is extremely intelligent. I did point out that the conclusion he reached would, in one sense, require that the coin had some kind of a memory. That is, it would have to realize that it would have to come up with more heads than tails during the next 100 flips in order to reach the expected number of heads (100) and the expected number of tails (100) after 200 flips.
Home  About Sanderson Smith  Writings and Reflections  Algebra 2  AP Statistics  Statistics/Finance  Forum
Previous Page  Print This Page
Copyright © 20032009 Sanderson Smith