CAIE S1 2020 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2020
SessionJune
TopicApproximating Binomial to Normal Distribution
TypeGeometric distribution probability

5 A pair of fair coins is thrown repeatedly until a pair of tails is obtained. The random variable \(X\) denotes the number of throws required to obtain a pair of tails.
  1. Find the expected value of \(X\).
  2. Find the probability that exactly 3 throws are required to obtain a pair of tails.
  3. Find the probability that fewer than 6 throws are required to obtain a pair of tails.
    On a different occasion, a pair of fair coins is thrown 80 times.
  4. Use an approximation to find the probability that a pair of tails is obtained more than 25 times.