Please help me write these in R script / Code

1, Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He then says to you, "Do you want to pick door #2?" What is the probability of winning the car if you use the strategy of first picking a random door and then switching doors every time? Note that the host will always open a door you did not pick, and it always reveals a goat.

2, A famous coin tossing game has the following rules: The player tosses a coin repeatedly until a tail appears or tosses it a maximum of 1000 times if no tail appears. The initial stake starts at 2 dollars and is doubled every time heads appears. The first time tails appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if tails appears on the first toss, 4 dollars if heads appears on the first toss and tails on the second, 8 dollars if heads appears on the first two tosses and tails on the third, and so on. Mathematically, the player wins 2k dollars, where k equals the number of tosses until the first tail. What is the probability of profit if it costs 15 dollars to participate?

3, In a random thirteen-card hand from a standard deck, what is the probability that none of the cards is an ace and none is a hear

4, In six coin tosses, what is the probability of having a different side come up with each throw, that is, that you never get two tails or two heads in a row

5, A random five-card poker hand is dealt from a standard deck. What is the chance of a flush (all cards are the same suit)?