Complexity Explorer Santa Few Institute

Question 1:

Since the coin is fair, the expected number of tails among a million tosses is 0.5 * 1,000,000 = 500,000. Note that this is also the expected number of heads.

Question 2: 

Recalling the formula given in the video for the actual number of tails, , where m is the expected number of tails (the same formula applies for heads too).

In the first part of the formula we find that by substituting the number for the expected number of  tails is  which is equal to which is equal to .

Thus, the difference between the actual and the expected number of tails will be approximately 500.