Concept explainers
A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, (V2, V3) might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day.
- a List the sample points in this experiment of ordering paper on two successive days.
- b Assume the vendors are selected at random each day and assign a
probability to each sample point. - c Let A denote the
event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P(A), P(B), P(A ∪ B), and P(A ∩ B) by summing the probabilities of the sample points in these events.
a.
List out the sample points for the given experiment by ordering paper on two successive days.
Answer to Problem 19E
The sample points for the given experiment by ordering paper on two successive days is
Explanation of Solution
Sample points:
When performing an experiment, it results with one or more outcomes. The possible outcomes in an experiment is called sample points. It is denoted by S.
In the given experiment, the possible outcomes by ordering paper on two successive days are
Therefore, the sample points for the given experiment by ordering paper on two successive days is
b.
Give a probability value to each of the sample points.
Answer to Problem 19E
The probability of each sample point is 0.1111.
Explanation of Solution
Probability:
For every event (say A) in sample space S, a number is called the probability of event A
It is assumed that the vendors are selected at random each day. Since it is random, the sample points are equally likely. From Part (a), it is clear that there are 9 sample points.
The probability of each sample point is calculated as follows:
Therefore, the probability of each sample point is 0.1111.
c.
Compute the probability for event
Answer to Problem 19E
The required probabilities are obtained as given below:
Explanation of Solution
It is clear from Part (a) that there are three favourable outcomes for event A and there are five favourable outcomes for event B. There are nine possible outcomes of this experiment.
The required probability for event A is computed as follows:
Therefore, the probability of event A is 0.3333.
The required probability for event B is computed as follows:
Therefore, the probability of event B is 0.5556.
The required probability for
Therefore, the probability of
The required probability for
Therefore, the probability of
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Chapter 2 Solutions
Mathematical Statistics with Applications
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