together. You can invite several friends simultaneously. Each one of them

independently has probability p to accept your invitation. How many friends

should you invite to maximize the probability that exactly one friend

accepts your invitation?*/

Suppose we invite n persons.

P=n*(1-p)^(n-1)*p //independently, sum

f(n)=ln(P)=ln(n)+(n-1)ln(1-p)+ln(p) //log

df/dn=1/n + ln(1-p) = 0 //derivative to get local max,

n = -1/ln(1-p) = 1/p; when x-->0, -ln(1-x) = x+x^2/2 + x^3/3 + ...

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