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Exam 5: Probability

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Question 101

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Club Members A survey of a club's members indicates that 50% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car. {Club Members Narrative} What is the probability that a club member owns neither a car nor a house?

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Question 102

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If P ( A ) = 0.35, P ( B ) = 0.45, and P ( A and B ) = 0.25, then P ( A | B ) is:

A) 1.4
B) 1.8
C) 0.714
D) 0.556

E) A) and B)
F) A) and C)

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Question 103

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A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5. Which of the following is a simple event?

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

Which of the following best describes the concept of marginal probability?

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 has a malignant cyst if he or she tests negative?

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

If two events are mutually exclusive their joint probability is ____________________.

If P ( A )= .30, P ( B )= .60, and P ( A and B )= .20, then P ( A | B )= .40.

If P ( A and B )= 1, then A and B must be mutually exclusive.

The collection of all the possible outcomes of a random experiment is called a sample space.

If P ( A )= 0.4 and P ( B )= 0.6, then A and B must be mutually exclusive.

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 P ( A and B ).

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

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} What proportion of accidents involved more than one vehicle?

The outcomes of a sample space must be ____________________ and ____________________.

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. {Hobby Shop Sales Narrative} What is the probability of selling at least two trucks in any given week?

Mutual Fund Price An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks, based past data. {Mutual Fund Price Narrative} Interpret the 75% probability.

The union of events A and B is the event that occurs when either A or B or both occur. It is denoted as ' A or B'.

Suppose P ( A )= 0.50, P ( B )= 0.40, and P ( B|A )= 0.30. a. Find P ( A and B ). b. Find P ( A or B ). c. Find P ( A|B ).