Question
A farmer is going to fence two equal adjacent parcels of land. These parcels share one side (which also requires fencing) as shown in the following diagram. The farmer has only 80 metres of fence.
(a) Write down the equation for the total length of the fence, \(80 \mathrm{~m}\), in terms of \(x\) and \(y\).
(b) Write down the total area of both parcels of land in terms of \(x\).
(c) Find the maximum area, in \(\mathrm{m}^2\), of one parcel of land.
Question
\(A\) and \(B\) are independent events such that \(\mathrm{P}\left(A \cap B^{\prime}\right)=0.09\) and \(\mathrm{P}\left(A^{\prime} \cap B\right)=0.49\).
Let \(x=\mathrm{P}(A \cap B)\).
(a) (i) Express \(\mathrm{P}(A)\) in terms of \(x\).
(ii) Express \(\mathrm{P}(B)\) in terms of \(x\).
(b) Find the value of \(x\).
(c) Find \(\mathrm{P}(B \mid A)\).