Consider a state lottery and the probability of winning the grand prize. The game is played by selecting a group of 6 numbers from {1, 2, 3, ..., 51), and the

state selects a group of 6 numbers from the same set. You win the grand prize if all 6 of your numbers match the state's. The probability of winning is so low that some people are trying different ways of increasing their odds. #1 Amir decides to increase his chance of winning by organizing N of his friends to buy one ticket each for this week's drawing. Each friend buys a ticket independently, and the minimum value of N (Nmin(epsilon)) to ensure that the probability that there is at least one winner among the group is greater than or equal to epsilon needs to be calculated for various values of epsilon. Write a Python function that calculates the value of Nmin(epsilon) for epsilon = 10-5, 10-3, 0.1, and 0.5. #2 If Amir has gathered enough friends to win with probability 0.5 using the above strategy, write a Python program that determines a way that they can increase their win probability above 0.5 without adding more people to the group.