6. A bag contains a large number of counters with one of the numbers 4,6 or 8 written on each of them in the ratio \(5 : 3 : 2\) respectively.
A random sample of 2 counters is taken from the bag.
- List all the possible samples of size 2 that can be taken.
The random variable \(M\) represents the mean value of the 2 counters.
Given that \(\mathrm { P } ( M = 4 ) = \frac { 1 } { 4 }\) and \(\mathrm { P } ( M = 8 ) = \frac { 1 } { 25 }\) - find the sampling distribution for \(M\).
A sample of \(n\) sets of 2 counters is taken. The random variable \(Y\) represents the number of these \(n\) sets that have a mean of 8
- Calculate the minimum value of \(n\) such that \(\mathrm { P } ( Y \geqslant 1 ) > 0.9\)