CAIE S1 2023 November — Question 5 5 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionNovember
Marks5
TopicGeometric Distribution
TypeGeometric then binomial separate scenarios

5 The probability that a driver passes an advanced driving test is 0.3 on any given attempt.
  1. Dipak keeps taking the test until he passes. The random variable \(X\) denotes the number of attempts required for Dipak to pass the test.
    1. Find \(\mathrm { P } ( 2 \leqslant X \leqslant 6 )\).
    2. Find \(\mathrm { E } ( X )\).
      Five friends will each take their advanced driving test tomorrow.
  2. Find the probability that at least three of them will pass tomorrow.
    75 people will take their advanced driving test next week.
    [0pt]
  3. Use an approximation to find the probability that more than 20 of them will pass next week. [5]