Person selected from combined populations

A single person or item is selected at random from the combined total of all populations, requiring weighted probabilities based on population sizes or proportions.

2 questions

CAIE S1 2008 June Q2
2 In country \(A 30 \%\) of people who drink tea have sugar in it. In country \(B 65 \%\) of people who drink tea have sugar in it. There are 3 million people in country \(A\) who drink tea and 12 million people in country \(B\) who drink tea. A person is chosen at random from these 15 million people.
  1. Find the probability that the person chosen is from country \(A\).
  2. Find the probability that the person chosen does not have sugar in their tea.
  3. Given that the person chosen does not have sugar in their tea, find the probability that the person is from country \(B\).
CAIE S1 2015 November Q2
2 In country \(X , 25 \%\) of people have fair hair. In country \(Y , 60 \%\) of people have fair hair. There are 20 million people in country \(X\) and 8 million people in country \(Y\). A person is chosen at random from these 28 million people.
  1. Find the probability that the person chosen is from country \(X\).
  2. Find the probability that the person chosen has fair hair.
  3. Find the probability that the person chosen is from country \(X\), given that the person has fair hair.