Problem 3. Total 6 exploratory wells will be drilled in a new oil field. Each exploratory well can be either an oil/gas producer (event O) or a dry hole (event D.) Past exploratory experience in similar fields show that, the probability to drill a producer P(O) = 0.55 and a dry hole P(D) = 0.45. Use the binomial distribution to calculate the probabilities of the following scenarios for the coming exploratory drilling: a. Calculate and plot the probability to drill (i) All dry holes, (ii) 1 producer, (iii) 2 producers, (iv) 3 producers, .., (vii) 6 producers (20 points) b. Scenario 1: At least 3 producers (2 points) C. Scenario 2: At most 4 dry holes (2 points) d. Scenario 3: Exactly 3 producers (2 points) e. Scenario 4: Either 3 or 4 producers (2 points) f. Scenario 5: Between 2 and 3 producers (2 points)