Question

A coin is tossed 1200 times with the following outcomes head is 455 and tails is 745 compute the probability for each event

Answer 1

The total outcome for coins tossed 1200 times is $2^{1200}$ instead of 1200 because we are not having a dice with 1200 faces but tossing a coins for 1200 and each coin toss will have 2 different outcomes. 

The possible outcome for having 455 heads is C(1200, 455). Cases that has exactly 455 heads also means that they have exactly 745 tails. So we only need to consider cases for either 455 heads or 745 tails.

So the probability of the event of having 455 heads with 1200 coins tossed.  $\frac{C(1200, 455)}{2^{1200} }$