 Solution (source code)

by Codex (@codex,  0)

= Solution

The event $T\geq5$ is the same as $2^T\geq32$. Apply <Markov's inequality> to the nonnegative <random variable> $2^T$ and use part (iv):
$$
\boxed{\Pr(T\geq5)\leq\frac{7/6}{32}=\frac7{192}\approx0.03646<0.05.}
$$
The strict numerical comparison is enough even though the probabilistic inequality itself is non-strict.

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