Concept explainers
Refer to the chance experiment described in the previous exercise and the
- a. List the outcomes in each of the following events. Which of these events are simple events? (Hint: See Example 6.3.)
- i. the
event that at least one car has an automatic transmission - ii. the event that exactly one car has an automatic transmission
- iii. the event that neither car has an automatic transmission
- i. the
- b. What outcomes are in the event B and C? In the event B or C?
6.3 Consider the chance experiment in which the type of transmission—automatic (A) or manual (M)—is recorded for each of the next two cars purchased from a certain dealer.
- a. What is the set of all possible outcomes (the sample space)? (Hint: See Example 6.2.)
- b. Display the possible outcomes in a tree diagram.
Example 6.3 Turning Directions
A traffic engineer has been asked to consider whether a stop sign at the bottom of a freeway off-ramp should be replaced by a traffic light. To help in this decision, she plans to observe traffic patterns for this off-ramp. Suppose she were to record the turning direction (L = left or R = right) of each of three successive vehicles. This is a chance experiment and the sample space contains eight outcomes;
Each of these outcomes determines a simple event. Other events include
A = event that exactly one of the cars turns right = {RLL, LRL, LLR}
B = event that almost one of the cars turns right - {LLL, RLL, LRL. LLR}
C = event that all cars turn in the same direction = {LLL, RRR}
Some other events that can be formed from the events just defined are
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Introduction To Statistics And Data Analysis
- The following description of the classic Linda Problem appeared in the New Yorker. In this experiment subjects are told, Linda is thirty-one years old, single outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with the issue of discrimination and social justice and also participated in antinuclear demonstrations. They are then asked to rank the probability of several possible descriptions of Linda today. Two of them are bank teller and bank teller and active in feminist movement. Many people rank the second event as more likely. Explain why this violates basic concepts of probability. Source: New Yorker.arrow_forwarda What is meant by an experiment? Sample space? b What is an event? c Define the probability of an event E in a sample space S in which all outcomes are equally likely. d What is the probability of the complement of E? e If a coin is tossed three times, what is the probability of getting all heads? At least one tail?arrow_forward
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