6 A survey is being carried out into the carbon footprint of individual citizens. As part of the survey, 100 citizens are asked whether they have attempted to reduce their carbon footprint by any of the following methods.
- Reducing car use
- Insulating their homes
- Avoiding air travel
The numbers of citizens who have used each of these methods are shown in the Venn diagram.
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One of the citizens is selected at random.
- Find the probability that this citizen
(A) has avoided air travel,
(B) has used at least two of the three methods. - Given that the citizen has avoided air travel, find the probability that this citizen has reduced car use.
Three of the citizens are selected at random.
- Find the probability that none of them have avoided air travel.
Section B (36 marks)