Exam 6: Probability

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

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The relative frequency approach to probability uses long term frequencies, often based on past data.

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A(n) ____________________ of a random experiment is a list of all possible outcomes of the experiment.

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Two events A and B are said to be mutually exclusive if P(A and B) = 1.0.

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If an experiment consists of five outcomes with P(O1) = 0.10, P(O2) = 0.20, P(O3) = 0.30, P(O4) = 0.25, then P(O5) is

(Multiple Choice)
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NARRBEGIN: Cysts 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.NARREND -{Cysts Narrative} In the absence of any test, what is the probability that the cyst is benign?

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Conditional probabilities are also called likelihood probabilities.

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NARRBEGIN: College Professorship 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.NARREND -Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A or B) = 0.30? Explain.

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If two events are collectively exhaustive, what is the probability that one or the other occurs?

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NARRBEGIN: Drunk Drivers 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: number of Vehieles inovelved Did alohol play a role? 1 2 3 Totals Yes 75 125 50 250 No 50 225 75 350 Totals 125 350 125 600 NARREND -{Drunk Drivers Narrative} What proportion of accidents involved alcohol or a single vehicle?

(Short Answer)
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NARRBEGIN: Marital Status Marital Status An insurance company has collected the following data on the gender and marital status of 600 customers. Marital Status Gender Single Maried Divorced Male 50 250 30 Female 100 100 40 Suppose that a customer is selected at random.NARREND -{Marital Status Narrative} Find the probability that the customer selected is a married female.

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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.

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If A and B are independent events with P(A) = 0.60 and P(A|B) = 0.60, then P(B) is:

(Multiple Choice)
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NARRBEGIN: Tea and Seltzer Tea and Seltzer Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both.NARREND -{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult drinks seltzer or tea or both?

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A random experiment is an action or process that leads to one of several possible ____________________.

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The probability of an event is the ____________________ of the probabilities of the simple events that constitute the event.

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NARRBEGIN: Drunk Drivers 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: number of Vehieles inovelved Did alohol play a role? 1 2 3 Totals Yes 75 125 50 250 No 50 225 75 350 Totals 125 350 125 600 NARREND -{Drunk Drivers Narrative} If 3 vehicles were involved, what proportion of accidents involved alcohol?

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Bayes' Law is used to compute:

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If A and B are any two events with P(A) = .8 and P(B|A) = .4, then P(A and B) is:

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If A and B are independent events with P(A) = 0.20 and P(B) = 0.60, then P(A|B) is:

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