Suppose you have two fair dice, each with 6 faces. One die is coloured blue and has the following faces: {1, 1, 1, 2, 2, 3}. The other die is coloured red, and has the following faces {1, 1, 2, 2, 3, 3}. You run an experiment where you throw each die once and record the results. 1: write out the sample space S for this experiment. If pBlue is the probability distribution for the blue die and pRed is the probability distribution for the red die, write out the probability distributions. 2: Let M be the event "The blue die is odd and the red die is even." Write out M and compute P(M). 3: Let N be the event "the sum of the dice is 5." Write out N and compute P(N). Are M and N Mutually exclusive? 4. Give an example of an event G such that G S and G is mutually exclusive to both M and N