5 Hugh owns a small farm.
\begin{enumerate}[label=(\alph*)]
\item He has two sows, Josie and Rosie, which he feeds at a trough in their field at 8.00 am each day.

The probability that Josie is waiting at the trough at 8.00 am on any given day is 0.90 . The probability that Rosie is waiting at the trough at 8.00 am on any given day is 0.70 when Josie is waiting at the trough, but is only 0.20 when Josie is not waiting at the trough.

Calculate the probability that, at 8.00 am on a given day:
\begin{enumerate}[label=(\roman*)]
\item both sows are waiting at the trough;
\item neither sow is waiting at the trough;
\item at least one sow is waiting at the trough.
\end{enumerate}\item Hugh also has two cows, Daisy and Maisy. Each day at 4.00 pm , he collects them from the gate to their field and takes them to be milked.

The probability, $\mathrm { P } ( D )$, that Daisy is waiting at the gate at 4.00 pm on any given day is 0.75 .\\
The probability, $\mathrm { P } ( M )$, that Maisy is waiting at the gate at 4.00 pm on any given day is 0.60 .\\
The probability that both Daisy and Maisy are waiting at the gate at 4.00 pm on any given day is 0.40 .\\
(i) In the table of probabilities, $D ^ { \prime }$ and $M ^ { \prime }$ denote the events 'not $D$ ' and 'not $M$ ' respectively.
\end{enumerate}

\hfill \mbox{\textit{AQA S1 2010 Q5 [11]}}