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  4. One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 the probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of p is :

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Q. One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 & the probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of p is :

Probability - Part 2

Solution:

Probability of 50 coins showing up heads = Probability of 51 coins showing up heads
$\Rightarrow { }^{100} C _{50} p ^{50}(1- p )^{50}={ }^{100} C _{51} p ^{51}(1- p )^{49} $
$\Rightarrow p =\frac{51}{101} $