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Understanding Statistical Probabilities of Observing Events

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1. Assume that company A makes 80% of all electrocardiograph machines, company B make 15% of them, and the company C makes the other 5%. The electrocardiographs machines made by company A have a 4% rate of defects, the company B machines have a 5% rate of defects, while the company C machines have a 8% rate of defects.
a) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the probability that is was made by company A.
b) If a randomly selected electrocardiograph machine is then tested and is found to be defective, find the probability that it was made by the com¬pany A.
c) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the probability that it was made by company A and it is defective.
d) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the probability that is was made by company A but it is not defective.

2. Police report that 88% of drivers stopped on suspicion of drunk driving are given a breath test, 15% a blood test, and 10% both tests. What is the probability that the next driver stopped on suspicion of drunk driving is given
i) at least one of the tests?
ii) a blood test or a breath test, but not both?
iii) neither test?
iv) Consider the two events given a blood test and given a breath test. Are the events independent? Are these disjoint events?

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Solution Summary

The probability of observing events is understood in the solution. Health applications are examined.

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1. Assume that company A makes 80% of all electrocardiograph machines, company B make 15% of them, and the company C makes the other 5%. The electrocardiographs machines made by company A have a 4% rate of defects, the company B machines have a 5% rate of defects, while the company C machines have a 8% rate of defects.
Let A be the event that company A makes a randomly selected machine
Let B be the event that company B makes a randomly selected machine
Let C be the event that company C makes a randomly selected machine
Let D be the event that a randomly selected machine is defective

The information given in the problem is summarized in the table ...

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