Apply <Markov inequality> to the nonnegative <random variable> $2^T$. On $\{T\geq5\}$ it is at least $32$, so
$$
\boxed{P(T\geq5)\leq\frac{\mathbb E(2^T)}{32}=\frac7{192}<0.05.}
$$
This exponential bound is substantially stronger here than applying <Markov inequality> directly to $T$.

Solution

Past exam of the options II course of the University of Oxford / 2011 / M / M4 / b / v / Solution

 Solution (source code)