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Define R for exactly the modeled interval
R=1+r is the positive risk-free factor from today to the claim expiry. An annual quotation is not automatically the rate for a shorter period. Convert it on an explicit convention before using this equation.
Match the underlying value
qSu+(1−q)Sd=S0R. Solving gives the pricing weight; the selected interior setup requires Sd<S0R<Su.
The weights price this model and do not estimate an observed state frequency.
Keep weighting and discounting separate
The original call amounts 30/0 and q=0.5 give a weighted expiry amount 15. Dividing by R=1.05 gives 14.285714 today. Omitting the final division reports a future weighted amount as a current price.
Keep contract assumptions compatible
The introductory application is one-period European expiry payoff with no underlying income and compatible frictionless financing. It does not accept an arbitrary actual-state probability as a substitute for q.