Edexcel S2 2018 October — Question 2

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2018
SessionOctober
TopicBinomial Distribution
TypeCombined probability with other distributions

  1. At a cafe, customers ordering hot drinks order either tea or coffee.
Of all customers ordering hot drinks, \(80 \%\) order tea and \(20 \%\) order coffee. Of those who order tea, \(35 \%\) take sugar and of those who order coffee \(60 \%\) take sugar.
  1. A random sample of 12 customers ordering hot drinks is selected. Find the probability that fewer than 3 of these customers order coffee.
    1. A randomly selected customer who orders a hot drink is chosen. Show that the probability that the customer takes sugar is 0.4
    2. Write down the distribution for the number of customers who take sugar from a random sample of \(n\) customers ordering hot drinks.
  2. A random sample of 10 customers ordering hot drinks is selected.
    1. Find the probability that exactly 4 of these 10 customers take sugar.
    2. Given that at least 3 of these 10 customers take sugar, find the probability that no more than 6 of these 10 customers take sugar.
  3. In a random sample of 150 customers ordering hot drinks, find, using a suitable approximation, the probability that at least half of them take sugar.