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Exam 5: Probability

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Question 91

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Messenger Service: Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time. -If a package was delivered on time, what is the probability that it was service A?

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P(A|O) = P...

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Question 92

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College Professorship: A Ph.D. graduate has applied for a job with two colleges: A and B. The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B. If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A. Let A = receiving an offer from college A, and let B = receiving an offer from college B. -What is the probability that at least one college will make her an offer?

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Question 93

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Initial estimates of the probabilities of events are known as:

Two events A and B are said to be independent if P(A|B) = P(B).

Suppose we have two events A and B. We can apply the addition rule to compute the probability that at least one of these events occurs.

Messenger Service: Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time. -Calculate P(B and O).

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

Hobby Shop Sales: Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks. -What is the probability of selling at least two trucks in any given week?

Drunk Drivers: Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: -What proportion of accidents involved more than one vehicle?

Equity Loan Rates: A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records. -What is the most common interest rate?

GPA and Class: A college professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors). One student is selected at random. -What is the probability that the student is in the upper class?

Cysts: After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient. -What is the probability that the patient has a malignant cyst if he or she tests negative?

If either event A or event B must occur, they are called mutually exclusive.

Drunk Drivers: Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: -Given alcohol was involved, what proportion of accidents involved a single vehicle?

We can apply the multiplication rule to compute the probability that two events occur at the same time.

Posterior probability of an event is the revised probability of the event after new information is available.

Events A and B are either independent or mutually exclusive.

GPA and Class: A college professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors). One student is selected at random. -What is the probability that the student is in the upper class and has GPA under 2.0?

Construction Bids: A construction company has submitted bids on two separate state contracts, A and B. The company feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B. Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract B. -What is the probability that the company will win at least one of the two contracts?

Hobby Shop Sales: Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks. -What is the probability of selling between 1 and 3 (inclusive) trucks in any given week?