CAIE S1 2023 June — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionJune
TopicGeometric Distribution
TypeP(X ≤ n) or P(X < n)

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.
  1. Find \(\mathrm { P } ( X = 4 )\).
  2. 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.
  3. 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 .
  4. For 9 randomly chosen spins of the two spinners, find the probability that the score is greater than 2 on at least 3 occasions.