Probability of coin tossing

[Akash Arjun]

A coin that comes up head with probability p>0  and tails with probability  (1-p)>0 independently on each flip is flipped eight times. Suppose the probability of three heads and five tails is  1/16 of the probability of five heads and 3 tails. Let  p=m/n where m and n are relatively prime positive integers. find m+n.

 

Please give a detailed explanation

[Shirsendu Roy]

 

(1-p)^{2}=p^{2}/16

or, 1-p=p/4

or, 1=p/4+p

or, 1=5p/4

or, p=4/5

or, 5+4=9

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