A box contains three black and four white chess pieces. Find the probability that a random selection of five chess pieces, taken one at a time without replacement, contains exactly two black pieces which are selected one immediately after the other.

The following table shows the numbers of IGCSE$\left(I\right)$ and $A$ Level $\left(A\right)$ examinations passed by a group of university students.

For a student selected at random, find:

$\mathrm{P}(\mathrm{I}+\mathrm{A}=11\mid \mathrm{A}<4)$

The following table shows the numbers of IGCSE$\left(I\right)$ and $A$ Level $\left(A\right)$ examinations passed by a group of university students.

For a student selected at random, find:

$\mathrm{P}(\mathrm{I}-\mathrm{A}>5\mid \mathrm{I}+\mathrm{A}>10)$

The following table shows the numbers of IGCSE$\left(I\right)$ and $A$ Level $\left(A\right)$ examinations passed by a group of university students.

Six students who all have at least three A Level passes are selected at random. Find the greatest possible range of the total number of IGCSE passes that they could have.