4 Each time Ben attempts to complete a crossword in his daily newspaper, the probability that he succeeds is \(\frac { 2 } { 3 }\). The random variable \(X\) denotes the number of times that Ben succeeds in 9 attempts.
- Find
(a) \(\mathrm { P } ( X = 6 )\),
(b) \(\mathrm { P } ( X < 6 )\),
(c) \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
Ben notes three values, \(X _ { 1 } , X _ { 2 }\) and \(X _ { 3 }\), of \(X\). - State the total number of attempts to complete a crossword that are needed to obtain three values of \(X\). Hence find \(\mathrm { P } \left( X _ { 1 } + X _ { 2 } + X _ { 3 } = 18 \right)\).