6. You performed two experiments. First, you toss a fair coin. Then, you roll a 6sided fair die (meaning each face is equally likely) with faces 1, 1,2,3,4, 5, where the two 1's are indistinguishable. (a) Write down the sample space (the order matters in this case). (b) Let A be the event that the outcome from the die is an odd number. Find A (as a subset of the sample space given in (a)). (c) Find the probability of A. 7. Show that P(A u B U C U D) =P(A) + P(B) + 13(0) + P(D) P(AnB) P(AnC') P(AnD) P(BC) P(BnD)P(CHD) +P(AanC)+P(AanD) +P(AnCnD)+P(BnCnD) 7P(ABOD)