CAIE A-Level Mathematics 5.4.2 Binomial and Geometric Distributions

CAIE A-Level Mathematics 5.4.2 Binomial and Geometric Distributions
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise recognising fixed-trial binomial and first-success geometric settings, stating B(n, p) or Geo(p) and calculating exact, cumulative or waiting-time probabilities.

How this is tested

  • choose B(n, p) for a fixed number of independent trials with constant success probability
  • choose Geo(p) when X counts the trial of the first success and use p(1 − p)^(r−1)
  • translate fewer than, at least or by a stated trial into the correct sum or complement

Question 1

[Maximum number: 3]

A coin is biased so that the probability of obtaining a head when it is thrown is 0.4. The coin is thrown repeatedly until the first head is obtained.

Question 1(a)

(a)

Find the probability that the first head is obtained on the 5th throw.

[ 1 ]

Question 1(b)

(b)

Find the probability that the first head is obtained after the 6th throw.

[ 2 ]