1. A bag contains a large number of counters with an odd number or an even number written on each.

Odd and even numbered counters occur in the ratio \(4 : 1\)
In a game a player takes a random sample of 4 counters from the bag.
The player scores
5 points for each counter taken that has an even number written on it
2 points for each counter taken that has an odd number written on it
The random variable \(X\) represents the total score, in points, from the 4 counters.

1. Find the sampling distribution of \(X\) A random sample of \(n\) sets of 4 counters is taken. The random variable \(Y\) represents the number of these \(n\) sets that have a total score of exactly 14
2. Calculate the minimum value of \(n\) such that \(\mathrm { P } ( Y \geqslant 1 ) > 0.95\)