5. A bag contains a large number of coins. It contains only \(1 \mathrm { p } , 5 \mathrm { p }\) and 10 p coins. The fraction of 1 p coins in the bag is \(q\), the fraction of 5 p 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 |
| \(\mathrm { P } ( M = m )\) | \(\frac { 1 } { 25 }\) | \(\frac { 13 } { 80 }\) | \(\frac { 319 } { 400 }\) |
- List all the possible samples of two coins which may be selected.
- Find the value of \(q\), the value of \(r\) and the value of \(s\)