Putnam 1968 B1

The temperatures in Chicago and Detroit are $x^\circ$ and $y^\circ$, respectively. These temperatures are not assumed to be independent; namely, we are given: \begin{itemize} \item[(i)] $P(x^\circ = 70^\circ)$, the probability that the temperature in Chicago is $70^\circ$, \item[(ii)] $P(y^\circ = 70^\circ)$, and \item[(iii)] $P(\max(x^\circ, y^\circ) = 70^\circ)$. \end{itemize} Determine $P(\min(x^\circ, y^\circ) = 70^\circ)$.