Explore BrainMass

Probability : Independent Events and Hemophilia

1.(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?

2. 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?


Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Problem #1
(a) Since , and are mutually independent, then we have
, ,
Thus we have

Thus is conditionally independent of given .
(b) No.

Problem #2
Let denote the event that Julie has ...

Solution Summary

Independent Events and Hemophilia are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.