- A bag contains a large number of counters with one of the numbers 5 , 10 or 20 written on each of them in the ratio \(5 : 2 : a\)
A jar contains a large number of counters with one of the numbers 5 or 10 written on each of them in the ratio \(1 : 3\)
One counter is selected at random from the bag and then two counters are selected at random from the jar.
The random variable \(R\) represents the range of the numbers on the 3 counters.
Given that \(\mathrm { P } ( R = 15 ) = \frac { 63 } { 256 }\)
- by forming and solving an equation in \(a\), show that \(a = 9\)
- find the sampling distribution of \(R\)