The probability distribution of a random variable \(X\) is shown in the table, where \(p\) is a constant.
\(x\)
0
1
2
3
\(P ( X = x )\)
\(\frac { 1 } { 12 }\)
\(\frac { 1 } { 4 }\)
\(p\)
\(3 p\)
Two values of \(X\) are chosen at random. Determine the probability that their product is greater than their sum.
A random variable \(Y\) takes \(n\) values, each of which is equally likely. Two values, \(Y _ { 1 }\) and \(Y _ { 2 }\), of \(Y\) are chosen at random.
It is given that \(\mathrm { P } \left( Y _ { 1 } = Y _ { 2 } \right) = 0.02\).
Find \(\mathrm { P } \left( Y _ { 1 } > Y _ { 2 } \right)\).