Prob of getting head and tail are p and 1-p resp..

 

Probability of getting head on exactly 50 out of the 100.. is

 

¹⁰⁰C₅₀ (p) ⁵⁰ (1-p)⁵⁰ 

 

And prob of getting head on 51 is ..

 

¹⁰⁰C₅₁ (p)⁵¹ (1-p)⁴⁹

 

so ,

¹⁰⁰C₅₀ (p) ⁵⁰ (1-p)⁵⁰  = ¹⁰⁰C₅₁ (p)⁵¹ (1-p)⁴⁹

 

=> 51(1-p) = 50p

 

=> p = 51/101

 

@ Anup..

prob of getting heads of exactly 50 is not p^50 since the positions of the heads can change ...so we have to multiply it by 100C50..this is binomial distribution method of finding the prob..direct qn!..asked in iitjee 1998..!!