\(
\eqalign{
& P_{eik} = pq^4 \cr
& P_{\neg eik} = (1 - p)(1 - q)^4 \cr
& P_R = \frac{{pq^4 }}
{{pq^4 + (1 - p)(1 - q)^4 }} \cr
& P_{q = \frac{1}
{2}} = \frac{{p\left( {\frac{1}
{2}} \right)^4 }}
{{p\left( {\frac{1}
{2}} \right)^4 + (1 - p)(1 - \left( {\frac{1}
{2}} \right))^4 }} \cr
& P_{q = \frac{1}
{2}} = \frac{p}
{{p + (1 - p)}} = p \cr}
\)