Probability of target shooting question

[pixel01]

Hi all,

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.

 

[robert Ihnot]

In the expansion p^n + n*p^(n-1) +++q^n, it is the first term that tells us the probability that all of the n shots would be successful. The next term tells us of one failue and n-1 successes. But those terms are not what we are looking for. So I think that's a start on the problem.