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 comÂ¬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.

When assigning probabilities of two simple events, can we assume that each event is always equally likely to occur and, thus assign .5 to each event? Could you provide an example in your explanation?

The Dept. of Labor has reported that 30% of the 2.1 million mathematical and computer scientists in the United States are women. If 3 individuals are randomly selected from this occupational group, and x = the number of females, determine P(x = 0), P(x = 1), P(x - 2), and P(x = 3).

Jared bets on the number 7 for each of 100 spins of a roulette wheel. Because P(7) = 1/38 he expects to win two or three times. What is the probability that Jared will actually win two or more times?
This was a quiz question I answered incorrectly, I want to understand how to get it if a similar question is on the mid term.

Let A and B be two events such that P(A) = 0.32 and P(B) = 0.41.
a. Determine the probability of the union of A and B given that A and B are mutually exclusive.
b. Determine the probability of the union of A and B given that A and B are independent.

Find the following probabilities:
a. Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.4 and P(A or B) = 0.9, find P(B).
b. Events A and B are defined on a common sample space. If P(A) = 0.20, P(B) = 0.40, and P(A or B) = 0.56, find P(A and B)

I would like some help with the following problems. Can I please get the actual manual work for the problems so I can follow the formula and follow the steps with other word problems. Thanks.
1. A normal population has a mean of 20.0 and a standard deviation of 4.0.
a. compute the z value associated with 25.0.
b. what prop

Suppose that A and B are independent events such that P(A) = 0.20 and P(B complement) = 0.70.
Find the probability of the intersection of A and B
Find the probability of the union of A and B

Let E and F be non-zero-probability events. If E and F are mutually-exclusive, can they also be independent? Explain the answer, and also prove it algebraically using the definitions of mutually-exclusive and independent events.

Please helps with the following problem.
1.) The special rule of addition is used to combine
a.) events that total more than one
b.) mutually exclusive events
c.) events based on subjective probabilities
d.) independent events
2) Events are independent if
a.) we can count the possible outcomes
b.) the pro