Problem

A bag contains a large number of coins. It contains only 1p, 5p and 10p coins.

The fraction of 1p coins in the bag is $q$, the fraction of 5p coins in the bag is $r$ and the fraction of 10p coins in the bag is $s$.

Two coins are selected at random from the bag and the coin with the highest value is recorded. Let $M$ represent the value of the highest coin.

The sampling distribution of $M$ is given below

$m$	1	5	10
$P(M = m)$	$\dfrac{1}{25}$	$\dfrac{13}{80}$	$\dfrac{319}{400}$

(a) List all the possible samples of two coins which may be selected.

(b) Find the value of $q$, the value of $r$ and the value of $s$.

(Total for Question 6 is 9 marks)