for 1000 stars, 50 tested:
Pi = prob(life on exactly i stars, given 0 on 50)
Pi = binomial(950,i) / 2^950
P = Sum(Pi; i=1..950)
P = Sum(binomial(950,i); i=1..950) / 2^950

for N stars, n tested:
Pi = prob(life on exactly i stars, given 0 on n)
Pi = binomial(N-n,i) / 2^(N-n)
P = Sum(Pi; i=1..(N-n))
P = Sum(binomial(N-n,i); i=1..(N-n)) / 2^(N-n)

Is that OK ? If so, now we need a formula for the sum.