Question

Of 70 tosses of a dime, 55 results are heads. Find the empirical probability of tossing heads with this coin. ______ Is this a fair coin, in your opinion? Why or why not?

Answer 1

The empirical, or experimental, probability of an event is the number of times the event occurred over the number of times the experiment was conducted.  In this case it would be 55/70 = 11/14, as there were 55 heads flipped out of a total of 70 coin flips.
Mathematically speaking, no, this is not a fair coin.  To be fair, both events would have to have the same chance of happening.  Since the probability of heads was 55/70, that leaves 15/70 for tails.  The chances are not equal, so not fair.