what is the probability of a successful transmission if exactly one station should transmit the data ?

Question

If there are n stations and each station can send data with probability n ,Now if at any instant of time there should be exactly one station which should transmit data then for finding the probability for this why can't I do p/np =1/n

since favourable case will be p since only 1 station will transmit and out of total cases to be np , what is wrong in this approach ?

Answer 1

if a station want to successfully transmit this is the probability 1/n . it is not the maximum probability but this is true. it can also be seen as Nc1 * p* (1-p)^(n-1). which is also equal to 1/n .

Comments

How is it equal to 1/n ?

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find the max value of p in the binomial equation above by finding its derivative and equating to 0 u will get p(max) = 1/n