# If you tossed a coin 10 times, what is the probability of landing on tails every time?

${\left(\frac{1}{2}\right)}^{10}$
Let $A = \left\{{a}_{1} , \ldots , {a}_{10}\right\}$ be the event of tossing a coin 10 times and landing on tails then we know that
$p \left(A\right) = p \left({a}_{1} \wedge {a}_{2} \wedge \ldots \wedge {a}_{10}\right) = p \left({a}_{1}\right) p \left({a}_{2}\right) \ldots p \left({a}_{10}\right)$ if they are mutually exclusive, which they are. the probability of landing on tails is $\frac{1}{2}$ which leads to
$\frac{1}{2} \cdot \frac{1}{2.} . . \cdot \frac{1}{2} = {\left(\frac{1}{2}\right)}^{10}$ or $\frac{1}{{2}^{10}}$