Edexcel S2 — Question 4

Exam BoardEdexcel
ModuleS2 (Statistics 2)
TopicBinomial Theorem (positive integer n)
TypeSubstitution into binomial expansion

4. Alison and Gemma play table tennis. Alison starts by serving for the first five points. The probability that she wins a point when serving is \(p\).
  1. Show that the probability that Alison is ahead at the end of her five serves is given by $$p ^ { 3 } \left( 6 p ^ { 2 } - 15 p + 10 \right) .$$
  2. Evaluate this probability when \(p = 0.6\).