The proportion of people in given community who have a certain disease is 0.005.

Question

The proportion of people in given community who have a certain disease is 0.005. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.01. Let A: a person tests positive and B: a person actually has the disease What is P(A)? What is P(A | B)? What is P(A B)? What is P(B|A)? Are events A and B statistically independent? Why? An extrusion die is used to produce aluminum rods. Specifications are given for the length and the diameter of the rods. For each rod, the length is classified as too short, too long, or OK, and the diameter is classified as too thin, too thick, or OK. In a population of 1000 rods, the number of rods in each class is follows: Let A be the event that the length of a randomly selected rod is OK, and let B be the event that the diameter of a randomly selected rod too thin. Determine the following probabilities: P(A B) P(A') P(A' B)

Explanation / Answer

A) i) P(A) =0.01 ii) P(A|B)=P(A)=0.01, since the event A is independentof the event B. iii) P(A and B)= P(A).P(B)=0.01*0.99=0.0099 iv)P(B|A)=P(B)=0.99 V) An event B is said to be independent of event A, ifP(B|A)=P(B); P(A) is not equal to zero. B) P(A or B)= P(A)+P(B)-P(A and B)=0.942+0.063-0.038=0.967 P(A')=1-P(A)=1-0.942=0.058 P(A' and B')=1-P(A or B)=1-0.967=0.033

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