The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

Probability of observing at least one head out of n tosses

$=1-\left(\frac{1}{2}\right)^{\mathrm{n}} \geq 0.9$

$\Rightarrow\left(\frac{1}{2}\right)^{\mathrm{n}} \leq 0.1$

$\Rightarrow n \geq 4$

$\Rightarrow$ minimum number of tosses $=4$