In the diagram, MK is a tangent to the circle at P, QRP = 50^ and SPK = 62^. Find QPS.

$P(\text{Mercy fails}) = 1 - P(\text{Mercy passes}) = 1 - \frac{2}{3} = \frac{1}{3}$
$P(\text{John fails}) = 1 - P(\text{John passes}) = 1 - \frac{5}{8} = \frac{3}{8}$
$P(\text{Alice fails}) = 1 - P(\text{Alice passes}) = 1 - \frac{3}{4} = \frac{1}{4}$

4. (c) Find the probability that only Mercy and John will pass the examination.

$P(\text{Mercy passes}) = \frac{2}{3}$
$P(\text{John passes}) = \frac{5}{8}$
$P(\text{Alice fails}) = \frac{1}{4}$ (from part b)

5. (a) In the diagram, $MK$ is a tangent to the circle at $P$, $\angle QRP = 50^\circ$ and $\angle SPK = 62^\circ$. Find $\angle QPS$.

The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
For tangent $PK$ and chord $PS$:

Arc $PQ$ subtends $\angle PRQ$ and $\angle PSQ$.

The sum of angles in a triangle is $180^\circ$.