= Solution
For binary traits, $Y_1Y_2$ is the indicator that both individuals are affected. Hence the pair probability is its <expectation>, or equivalently the <covariance> plus the product of individual means. Using the preceding results,
$$
\boxed{\Pr(Y_1=Y_2=1\mid J=2)=p^2\beta^2,\qquad
\Pr(Y_1=Y_2=1\mid J=0)=p^2\alpha^4.}
$$
These statements retain the same conditional-independence and common-population assumptions as the <multiplicative diallelic penetrance> covariance calculation.
Back to article page
