I got the following two questions which I have no clue how to do it.

(1)There are three coins in a barrel. These coins when flipped will come up heads with respective probabilities 0.3, 0.5 and 0.7. A coin is randomly selected from among these three coins and is then flipped until a head appears. Let N denote the number of flips necessary.

What is the probability that N = n, n = 1, 2, 3, . . .?

Is N a geometric random variable?

Suppose now that each time a coin is flipped, it is returned to the barrel and a coin is then selected at random from the three coins, what is the distribution of N?

(2) The number of fish that a fisherman catches in a day is a Poisson random variable with mean 30. On average the fisherman throws back two out of every three fish he catches.

Find the probability that, on a given day, the fisherman takes home k fish, stating any independence assumptions that you make.

Can anyone give me some hints please?

Thank you so much