Weights from a pair of digitals

An index will finish a year from now either above a level or at or below it. Today a contract paying $100$ in a year if it finishes above has a fair mid of $46$, and a contract paying $100$ in a year if it finishes at or below has a fair mid of $50$. No interest rate is quoted: the one-year discounting is whatever these $2$ prices imply, since together the contracts pay $100$ for certain. The risk-neutral probability is the one under which each price equals the discounted expected payoff. What is the risk-neutral probability that the index finishes above? Give an exact fraction.

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