Understanding Statistical Probabilities of Observing Events 1 Assume that company A makes 80% of all

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?

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