Man claims that he can find oil with a magic stick. Laboratory wants to test this so they setup two barrels. One barrel has oil and one doesn't. They give the man 10 tries. a) Let X be the amount of correct choices ( man chooses the barrel with oil). If there is a probability of 0,8 that the man finds oil, what is the distribution of X, E[X] and variance Var[x]? b) If there is a probability of 0,8 that the man finds oil, what is the probability that he chooses the correct barrel (oil barrel) at least 8 times? c) What would be the probability to choose the correct barrel at least 8 times, if he just randomly picks the barrel?