AIDS Test - HIV Infection - Probability Theory - Birth of Boys and Girls - Independent Variables - Statistics Assignment Help

Assignment Task:

Probability Theory Statistics Assessment Answer

Question

1. An AIDS test can detect an HIV infection with 99?curacy, whereas it can accurately identify the absence of infection with 98% probability. Noting that approximately 0.6% of the US population is infected by HIV, how likely is it that a positive AIDS test indicates indeed an HIV infection?

2. Assume that you have two urns and a fair die. The first urn contains 6 red and 2 black balls, the second urn 3 red and 7 black balls. We roll the die and if it shows a 1 or 2, we pick a ball from the first urn, and if it shows a 3, 4, 5 or 6 we pick a ball from the second urn.

i) What is the probability that the drawn ball is red?

ii) If we know that a drawn ball is red, what is the probability that it came from the first urn?

3. Assume that in a family the birth of a boy and a girl is equally likely and that the family has n ≥ 2 children. Are the events

A . . . There is at least one boy and at least one girl in the family

B . . . There is at most one girl in the family

independent?

4. Let A, B and C be three independent events in a sample space ? and define E = A ∪ B. Show that also the events E and C are independent.