# What is the most probable number of heads out of 50 tosses of a fair coin (A) 15, (B) 25 (C) 35 ?

May 8, 2016

(B) $25$ times

#### Explanation:

The most probable outcome is (B) $25$ times - half of the times heads, half of the time tails.

However, the probability of it being exactly $25$ heads out of $50$ tosses is:

(((50),(25)))/2^50 = (50!)/((25!)(25!)2^50) = 15801325804719/140737488355328 ~~ 0.112275

that is about 11%.

The next most probable outcomes are (A) 15 and (C) 35, both of which have probability:

(((50),(15)))/2^50 = (50!)/((15!)(35!)2^50) = 140676848445/70368744177664 ~~ 0.002

that is about 0.2%