Conditional probability with geometric

Find conditional probabilities involving geometric distributions (e.g., given that X = n, find probability of another event).

1 questions

OCR Further Statistics Specimen Q6
6 A bag contains 3 green counters, 3 blue counters and \(w\) white counters. Counters are selected at random, one at a time, with replacement, until a white counter is drawn.
The total number of counters selected, including the white counter, is denoted by \(X\).
  1. In the case when \(w = 2\),
    (a) write down the distribution of \(X\),
    (b) find \(P ( 3 < X \leq 7 )\).
  2. In the case when \(\mathrm { E } ( X ) = 2\), determine the value of \(w\).
  3. In the case when \(w = 2\) and \(X = 6\), find the probability that the first five counters drawn alternate in colour.