A recent study¹ of college graduates in the United states discovered that approximately 60% of degree holders would "change their majors if they could go back to school" and re-do their undergraduate degree. Let's presume this proportion also holds for Canadian undergraduate university degree holders.

One randomly selects two Canadians who hold an undergraduate degree. Compute the probability that

Compute the probability that

1. both would change their undergraduate major (if they had the ability for a re-do).

2. neither would change their undergraduate major (if they had the ability for a re-do).

3. at least one of the two would change their undergraduate major (if they had the ability for a re-do).

4. Suppose you are to randomly pick nn-Canadians with undergraduate degrees in such a way that the probability of at least one of them would change their undergraduate degree is 0.95. Compute the minimum number of Canadians with undergraduate degrees you would have to randomly select. In other words, compute the sample size nn. (Hint: ln(ab)=bln(a)ln(ab)=bln(a)...)