6. At a men's tennis tournament there are 3 , 4 or 5 sets in a match.
Over many years, data collected show that 50\% of matches last for exactly 3 sets, 30\% of matches last for exactly 4 sets and 20\% of matches last for exactly 5 sets.
A random sample of 3 tennis matches is taken. The number of sets in each match is recorded as \(S _ { 1 } , S _ { 2 }\) and \(S _ { 3 }\) respectively.
The random variable \(M\) represents the maximum value of \(S _ { 1 } , S _ { 2 }\) and \(S _ { 3 }\)
- List all the samples where \(M \neq 5\)
- Find the sampling distribution of \(M\)
- Write down the mode of \(S _ { 1 }\) and the mode of \(M\)