5. A biased spinner can only land on one of the numbers \(1,2,3\) or 4 . The random variable \(X\) represents the number that the spinner lands on after a single spin and \(\mathrm { P } ( X = r ) = \mathrm { P } ( X = r + 2 )\) for \(r = 1,2\)
Given that \(\mathrm { P } ( X = 2 ) = 0.35\)
- find the complete probability distribution of \(X\).
Ambroh spins the spinner 60 times.
- Find the probability that more than half of the spins land on the number 4 Give your answer to 3 significant figures.
The random variable \(Y = \frac { 12 } { X }\)
- Find \(\mathrm { P } ( Y - X \leqslant 4 )\)