CAIE S1 2024 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2024
SessionJune
TopicDiscrete Probability Distributions
TypeConstruct probability distribution from scenario

6 Harry has three coins:
  • One coin is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 3 }\).
  • The second coin is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 4 }\).
  • The third coin is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 5 }\).
Harry throws the three coins. The random variable \(X\) is the number of heads that he obtains.
  1. Draw up the probability distribution table for \(X\).
    Harry has two other coins, each of which is biased so that the probability of obtaining a head when it is thrown is \(p\). He throws all five coins at the same time. The random variable \(Y\) is the number of heads that he obtains.
  2. Given that \(\mathrm { P } ( Y = 0 ) = 6 \mathrm { P } ( Y = 5 )\), find the value of \(p\).