Question: Consider rolling two fair dice. Let A be the event that the first die is greater than 4. Let B be the event that the

Consider rolling two fair dice. Let A be the event that the first die is greater than 4. Let B be the event that the sum of the two dice is 6. Let C be the event that the sum of the two dice is 7.

  1. Find P(A).
  2. Find P(B)
  3. Find P(C).
  4. Find P(B|A).
  5. Find P(A|B).
  6. Find P(C|A).
  7. Find P(A|C).
  8. Find P(AB).
  9. Find P(AUB).
  10. Find P(AC).
  11. Find P(AUC).
  12. Are the events A and B mutually exclusive?
  13. Are the events B and C mutually exclusive?
  14. Are the events A and B independent?
  15. Are the events A and C independent?
  16. Are the events B and C independent?

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