Hey MartinDalskov.

For a) you need to consider what the confidence interval represents: a 95% interval represents that 95% of the time the interval will contain the true parameter.

Now if something is independent, you need to consider the independence criterion which is P(A and B) = P(A)P(B). So if you have the probability of one interval containing the true parameter, then you have to consider the probability corresponding to your statement (i.e. what you expect actually to include the true value) and then find the frequency (which is multiplying this probability by the number of items in your population which in this case is 20 intervals).

Part b) is the same but consider the extension to twenty variables of P(A and B) = P(A)P(B) for independent A and B (except that we have twenty intervals not two).