11 In this question you must show detailed reasoning.
A biased four-sided spinner has edges numbered \(1,2,3,4\). When the spinner is spun, the probability that it will land on the edge numbered \(X\) is given by
\(P ( X = x ) = \begin{cases} \frac { 1 } { 2 } - \frac { 1 } { 10 } x & x = 1,2,3,4 ,
0 & \text { otherwise } . \end{cases}\)
- Draw a table showing the probability distribution of \(X\).
The spinner is spun three times and the value of \(X\) is noted each time.
- Find the probability that the third value of \(X\) is greater than the sum of the first two values of \(X\).