Exam 5: Probability

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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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sum

If A and B are any two events with P ( A )= .8 and P ( B|A c)= .7, then P ( Ac and B )is

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B

The conditional probability of event B given event A is denoted by P ( A | B ).

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The outcomes of a sample space must be ____________________, which means that all possible outcomes must be included.

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

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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: 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:   {Drunk Drivers Narrative} If multiple vehicles were involved, what proportion of accidents involved alcohol? {Drunk Drivers Narrative} If multiple vehicles were involved, what proportion of accidents involved alcohol?

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

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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. {Cysts Narrative} What is the probability that the patient will test negative?

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If A and B are independent, then P ( A | B )= P ( A )or P ( B | A )= P ( B ).

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If P ( A )= 0.25 and P ( B )= 0.65, then P ( A and B )is:

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

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The probability of the intersection is called a joint probability.

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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. {Messenger Service Narrative} If a package was delivered on time, what is the probability that it was service A ?

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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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Financial Consultants A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table: Financial Consultants A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:   One client is selected at random, and two events A and B are defined as follows: A : The client selected is male. B : The client selected has a balanced portfolio. {Financial Consultants Narrative} Find the following probabilities:   a. P ( A|B )  b. P ( B|A ) One client is selected at random, and two events A and B are defined as follows: A : The client selected is male. B : The client selected has a balanced portfolio. {Financial Consultants Narrative} Find the following probabilities: a. P ( A|B ) b. P ( B|A )

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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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Certification Test A standard certification test was given at three locations. 1,000 candidates took the test at location A , 600 candidates at location B , and 400 candidates at location C . The percentages of candidates from locations A , B , and C who passed the test were 70%, 68%, and 77%, respectively. One candidate is selected at random from among those who took the test. {Certification Test Narrative} What is the probability that the selected candidate passed the test?

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{Certification Test Narrative} What is the probability that the selected candidate took the test at location C and failed?

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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 . {Construction Bids Narrative} What is the probability that the company will win at least one of the two contracts?

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Two or more events are said to be independent when the occurrence of one event has no effect on the probability that another will occur.

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