1) A math game is played with 2 fair number cubes. A green cube is numbered 1 through 3, and each number is marked on 2 faces. A red cube has faces numbered 1 through 6. If both cubes are tossed, what is the probability of rolling a 3 on the green cube and a 6 on the red cube?

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.