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Understanding Statistical Probabilities of Observing Events

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?

Solution Preview

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 ...

Solution Summary

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

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