Question:
A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of $\mathrm{n}$ is_________.
Solution:
$\mathrm{P}($ Head $)=\frac{1}{2}$
$1-\mathrm{P}($ All tail $) \geq 0.9$
$1-\left(\frac{1}{2}\right)^{\mathrm{n}} \geq 0.9$
$\Rightarrow\left(\frac{1}{2}\right)^{\mathrm{n}} \leq \frac{1}{10}$
$\Rightarrow \mathrm{n}_{\min }=4$
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