= Solution
Let $b$ and $h$ be the numbers of units of the <numéraire> and the <stock> in a <replicating strategy>. The two terminal payoffs of the <European call option> are $2$ and $0$, so
$$
15b+20h=2,\qquad20b+15h=0.
$$
Solving these simultaneous equations gives $b=-6/35$ and $h=8/35$. \b[The initial replication cost is]
$$
\boxed{C(1,18)=10b+10h=\frac47.}
$$
As an independent pricing check, let $q$ be the <risk-neutral probability> of the state $(15,20)$ under the <numéraire> measure. The discounted <stock> must have initial value one and terminal mean one:
$$
1=q\frac{20}{15}+(1-q)\frac{15}{20},\qquad q=\frac37.
$$
<Risk-neutral valuation> then gives $10(3/7)(2/15)=4/7$. The physical probabilities $1/2,1/2$ are not the <numéraire>-measure probabilities.
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