Three Quotes That Sum Wrong

A bookmaker posts decimal odds on a match with exactly three outcomes -- a stake of $\$1$ at decimal odds $d$ returns $\$d$ in total if the outcome hits, and nothing otherwise.

$$\text{Home } 2.10, \qquad \text{Draw } 4.00, \qquad \text{Away } 4.20.$$

(a) Is there a risk-free profit here? Show how you know in one line. (b) With $\$1{,}000$ to deploy, how do you split it, and what do you make? (c) A second book posts odds whose implied probabilities sum to $1.05$. What does that number mean, and why is the situation in (a) so rare in practice?