Solution
= Solution
{c}
By the <law of total probability>,
$$
\mathbb P(T=1)=\frac16\sum_{r=1}^6\frac{7-r}{6}=\frac7{12}.
$$
<Bayes' theorem> therefore gives the <conditional probability mass function>
$$
\boxed{\mathbb P(R=r\mid T=1)
=\frac{(1/6)(7-r)/6}{7/12}=\frac{7-r}{21},\quad r=1,\ldots,6.}
$$
The six <probabilities> sum to one. A small red outcome is more likely after an immediate success because more white faces can meet its threshold.