There is a market for bets on the outcome of a coin toss. The possible outcomes are heads, tails, and edge. There are three assets traded in that market:

Asset A pays $1 independent of the outcome

Asset B pays $1.50 for a head and $0 for tails and $1 if the coin lands on its edge

Asset C pays $10 if and only if the coin lands on its edge (and $0 otherwise).

The prices of those assets are always constant and fixed at $1. We assume that the payments to the winning bidders take place immediately after the outcome is determined.

(a) What is the implied risk-free interest rate in this market?

(b) What are the risk-neutral probabilities of each of the possible coin toss outcomes (heads, tail, edge)?