Assignment:
Q1.(a) Let. A, B, C are mutually independent. Prove that A. is conditionally independent of B given C.
(b) Assume that A, B are both independent and conditionally independent given C. Is it necessary that A, B, C are mutually independent?
Q2. Hemophilia is a hereditary disease. If a mother has it, then with probability 1/2, any of her sons independently will inherit it. Otherwise, none of the sons will become heniophilic. Julie is a mother of two sons and from her medical history it is known that, with probability 1/4, she is hemophilic. That is the probability that
(a) her first son is hemophilic;
(h) her second son is hemophilic;
(c) both sons are hemophilic?
Cards are drawn at random from an ordinary deck of 52 cards, one- by-one without replacement. What is the probability that no heart is drawn before the ace of spades is drawn?
Provide complete and step by step solution for the question and show calculations and use formulas.