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

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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%#