A student flips a fair penny several times and records the
number of tails in a table. The letter n represents the
number of times the student tossed the coin. One table shows
experimental results (generated by a computer), and the other table
shows phony data (generated by the author). Identify the table with
the experimental results and explain how you decided the other
table consists of phony data.

A student flips a fair penny several times and records the number of tails in a...
Suppose we flip a fair coin n times. We say that the sequence is balanced when there are equal number of heads and tails. For example, if we flip the coin 10 times and the results are HT HHT HT T HH, then this sequence balanced 2 times, i.e. at position 2 and position 8 (after the second and eighth flips). In terms of n, what is the expected number of times the sequence is balanced within n flips?