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)= nCr pr qn-r
P(x=50)= 100C50 p50 q50
(1)
P(x=51)= 100C51 p51 q49
(2)
Equate both equations;
51-51p = 50 p
101 p = 51
1