3. 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. (i) Explicitly write out the sample space S for this experiment. If pB is the probability distribution for the blue die and pr is the probability distribution for the red die, write out the probability distributions. (ii) Let E be the event "The blue die is odd and the red die is even." Write out E and compute P (E). (iii) Let F be the event "the sum of the dice is 5." Write out F and compute P (F ). Are E and F mutually exclusive? (iv) Give an example of an event G such that G C S and G is mutually exclusive to both E and F Explain each step thoroughly