This needs to be answered both mathematically and also using R programming

Problem 2. (25 points) Recall the experiment we performed in the recitation. Assume an urn c0ntains 12 balls, 8 of which are white balls and 4 are black balls. In this problem we pick samples of balls at random from the urn. (a) If we pick a single ball from the urn, what is the probability it is a white ball? What about the probability of drawing a black ball? (b) If we draw a ball 4 times with replacement (each time the ball is returned to the urn after recording its color), what is the probability of drawing a black balls exactly twice? (c) If we draw a sample of 3 balls (i.e., picking without replacement) and given that the rst two balls selected were a black ball and a white ball, what is the conditional probability of the third ball drawn being white? (d) If we pick 5 without replacement what is the probability that at least 2 of the 5 are black