CAIE S1 2020 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2020
SessionNovember
TopicDiscrete Probability Distributions
TypeConstruct probability distribution from scenario

6 Three coins \(A , B\) and \(C\) are each thrown once.
  • Coins \(A\) and \(B\) are each biased so that the probability of obtaining a head is \(\frac { 2 } { 3 }\).
  • Coin \(C\) is biased so that the probability of obtaining a head is \(\frac { 4 } { 5 }\).
    1. Show that the probability of obtaining exactly 2 heads and 1 tail is \(\frac { 4 } { 9 }\).
The random variable \(X\) is the number of heads obtained when the three coins are thrown.
  • Draw up the probability distribution table for \(X\).
  • Given that \(\mathrm { E } ( X ) = \frac { 32 } { 15 }\), find \(\operatorname { Var } ( X )\).