Question

Make a decision about the given claim. do not use any formal procedures and exact calculations. use only the rare event rule. ​claim: a coin favors heads when​ tossed, and there are 11 heads in 20 tosses.

Answer 1

You would expect that if a coin were fair the number of times heads appears would equal the number of times tails appears for a certain number of tosses. So for 20 tosses we would expect 10 and 10. However, this is a mathematical reality and not necessarily what we would see if we actually toss the coin 20 times. In fact this half and half situation becomes more and more the case if we flip the coin a large number of times (a very, very large number of times). 20 is not a very large number of times. If the coin lands heads up 11 of 20 times, it is most likely still fair and not really favoring heads. So the claim is false.

It is only in cases where we see a very high number of heads in comparison with tails (a large discrepancy between the two) that we might start to wonder if the coin is indeed fair.