5 In a recent report, it was stated that \(40 \%\) of working people have a degree. For the whole of this question, you should assume that this is true. A researcher wishes to interview a working person who has a degree. He asks working people at random whether they have a degree and counts the number of people he has to ask until he finds one with a degree.

1. Find the probability that he has to ask 5 people.
2. Find the mean number of people the researcher has to ask. Subsequently, the researcher decides to take a random sample from the population of working people.
3. A random sample of 5 working people is chosen. What is the probability that at least one of them has a degree?
4. How large a random sample of working people would the researcher need to take to ensure that the probability that at least one person has a degree is 0.99 or more?