50% chance a bomb hits target; at least 2 hits needed to destroy.

Question

50\% chance a bomb hits target; at least 2 hits needed to destroy. Find minimum bombs for $\ge99\%$ chance of destruction.

Answer: 11

Accepted Answer

$$1-{}^nC_1\left(\frac12\right)^n-\left(\frac12\right)^n \ge 0.99 \implies \frac{n+1}{2^n}\le0.01 \implies n\ge11$$

Solutions · 1