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

Question

3247 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-08T22:06:10

(B) $25$ times

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 $0.2%$

What is the most probable number of heads out of 5050 tosses of a fair coin (A) 1515, (B) 2525 (C) 3535 ?