= Solution
The <Markov inequality> states that for a nonnegative <random variable> $Z$ and $a>0$,
$$
\mathbb P(Z\geq a)\leq\frac{\mathbb E[Z]}a.
$$
Because $T$ is integer-valued, apply it with $a=1$. With $p=n^{-\alpha}$,
$$
\mathbb P(T>0)=\mathbb P(T\geq1)\leq\binom n3 n^{-3\alpha}\leq\frac16n^{3-3\alpha}\longrightarrow0\quad(\alpha>1).
$$
Therefore
$$
\boxed{\mathbb P(T=0)\longrightarrow1.}
$$
This is the <first moment method>: if the expected <triangle count in a binomial random graph> tends to zero, triangles occur with vanishing probability.
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