\[\begin{align} p(T_{10} \mid T_{1\ldots9}) &amp;= \frac{p(T_{10} \wedge T_{1\ldots9})}{p(T_{1\ldots9})}\\ &amp;= \frac{p(T_{1\ldots10})}{p(T_{1\ldots10} \vee [T_{1\ldots9} \wedge H_{10}])}\\ &amp;= \frac{p(T_{1\ldots10})}{p(T_{1\ldots10}) + p(T_{1\ldots9} \wedge H_{10})}\\ &amp;= \frac{1/11}{1/11 + 1/110}\\ &amp;= \frac{10}{11}\end{align}\]