4 A fair 5 -sided spinner has sides labelled 1, 2, 3, 4, 5. The spinner is spun repeatedly until a 2 is obtained on the side on which the spinner lands. The random variable \(X\) denotes the number of spins required.
- Find \(\mathrm { P } ( X = 4 )\).
- Find \(\mathrm { P } ( X < 6 )\).
Two fair 5 -sided spinners, each with sides labelled \(1,2,3,4,5\), are spun at the same time. If the numbers obtained are equal, the score is 0 . Otherwise, the score is the higher number minus the lower number. - Find the probability that the score is greater than 0 given that the score is not equal to 2 .
The two spinners are spun at the same time repeatedly . - For 9 randomly chosen spins of the two spinners, find the probability that the score is greater than 2 on at least 3 occasions.