Bomb The Target!!

For n bombs there is a probability of (n+1)/2^n not hitting the target.

When n>=11 p<1%

Probability of hitting $\geq 99\%\Rightarrow$

Probability of not hitting $\leq 1\%=0.01$

Probability that none of $n$ shots will hit $=\dfrac{1}{2^n}$

Probability that exactly one will hit $=\dbinom{n}{1}\dfrac{1}{2^n}$

$\dfrac{(1+n)}{2^n}\leq 0.01$ $\Rightarrow n\geq 11$

Using Python and Monte Carlo sampling:

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import random
drops = 0
trials = 100000
probability = 0.0
while probability < 0.99:
    yes = 0.0
    drops += 1
    for i in xrange(trials):
        hits = 0
        for i in xrange(drops):
            if random.choice((True, False)):
                hits += 1
            if hits == 2:
                yes += 1
                break
    probability = yes/trials
    print drops, probability
print "Answer:", drops