Astronomer's estimate

I am trying to solve the problem but end up with no where, Please help me to solve the problem

Astronomers estimate that as many as one hundred billion stars in the MilkyWay galaxy are encircled by planets. If so, we may have a plethora of cosmic neighbors. Let
p denote the probability that any such solar system contains intelligent life. How small can p be and still give a fifty-fifty chance that we are not alone?

Thanks in advance
I have tried to solve the problem as

Here total number of stars is 10 to the power 11, Now the Poisson limit to find the required probability and equalizing it with 0.5(fifty- fifty chance) can give the value of smallest p(probability), but in that case, what will be the value of K, as given in the Poisson limit theorem.


New Member
You only need the K = 0 (degenerate) result of the Poisson Distribution. Set that result to 0.5 to solve for lamda, then p.