2 A market researcher wants to interview people who watched a particular television programme. Audience research data used by the broadcaster indicates that \(12 \%\) of the adult population watched this programme. This figure is used to model the situation.
The researcher asks people in a shopping centre, one at a time, if they watched the programme. You should assume that these people form a random sample of the adult population.

1. Find the probability that the fifth person the researcher asks is the first to have watched the programme.
2. Find the probability that the researcher has to ask at least 10 people in order to find one who watched the programme.
3. Find the probability that the twentieth person the researcher asks is the third to have watched the programme.
4. Find how many people the researcher would have to ask to ensure that there is a probability of at least 0.95 that at least one of them watched the programme.