 Solution

Write $b$ for transmission of allele 1 with allele 2 untransmitted, and $c$ for the reverse. The informative transmissions give $b=20$, $c=30$. Under the fair-transmission null, conditional on $b+c=50$, $b$ is binomial with success probability $1/2$. Its standardized squared deviation isThe reference distribution is asymptotically chi-squared with one degree of freedom, giving a two-sided $p$-value about $0.157$. Allele 2 is overtransmitted and hence is the allele more associated with disease in this sample, although this result is not strong evidence against the null. The diagonal transmission cells contribute no discordant contrast.