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9

Mark the correct alternative in the following:

One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

Given:

n=100

p(H)=P(T)=1/2

P(x=r)= ^{n}C_{r} p^{r} q^{n-r}

P(x=50)= ^{100}C_{50} p^{50} q^{50}

(1)

P(x=51)= ^{100}C_{51} p^{51} q^{49}

(2)

Equate both equations;

51-51p = 50 p

101 p = 51

1