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It's rather long time I haven't dealt with maths. Now I have this problem.

A man can shoot right on the target with the probability of success of p = 30%. The question is how many shots does he need to shoot to be 95% (P) successful.

My idea is :

Let n the number of shots needed. Then P = p^n+p^(n-1)*q+p^(n-2)*q^2....+p*q(n-1)

where q=1-p.

Am i right and if yes, how can I shorten the result?

Thanks for any help.