CAIE S1 2019 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2019
SessionNovember
TopicConditional Probability
TypeProbability distribution from conditional setup

6 A box contains 3 red balls and 5 white balls. One ball is chosen at random from the box and is not returned to the box. A second ball is now chosen at random from the box.
  1. Find the probability that both balls chosen are red.
  2. Show that the probability that the balls chosen are of different colours is \(\frac { 15 } { 28 }\).
  3. Given that the second ball chosen is red, find the probability that the first ball chosen is red.
    The random variable \(X\) denotes the number of red balls chosen.
  4. Draw up the probability distribution table for \(X\).
  5. Find \(\operatorname { Var } ( X )\).