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)? O Sample space = {A, M, AM) Sample space = {A, M, AA, AM, MA, MM> Sample space= (AA, AM, MM) Sample space= (AA, AM, MA, MM) Sample space (A, M) (b) Display the possible outcomes in a tree diagram. (Do this on paper. Your instructor may ask you to turn in this sketch.) (c) List the outcomes in each of the following events.
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)? O Sample space = {A, M, AM) Sample space = {A, M, AA, AM, MA, MM> Sample space= (AA, AM, MM) Sample space= (AA, AM, MA, MM) Sample space (A, M) (b) Display the possible outcomes in a tree diagram. (Do this on paper. Your instructor may ask you to turn in this sketch.) (c) List the outcomes in each of the following events.
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 4SE: What is the difference between events and outcomes? Give an example of both using the sample space...
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Question
![**Title: Understanding Transmission Type Outcomes in Probability**
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)?**
- Sample space = {A, M}
- Sample space = {A, M, AA, AM, MA, MM}
- Sample space = {AA, AM, MM}
- Sample space = {AA, AM, MA}
- Sample space = {A, M}
**(b) Display the possible outcomes in a tree diagram.** (Visual representation required; this step encourages drawing a tree diagram on paper.)
**(c) List the outcomes in each of the following events.**
**I. B, the event that at least one car has a manual transmission**
- {AM, MA}
- {AA}
- {MM}
- {AM, MA, AA}
- {MM, AM, MA}
**II. C, the event that exactly one car has an automatic transmission**
- {AA, AM, MA}
- {AA}
- {MM}
- {AM, MA}
- {AM, MA, MM}
**III. D, the event that neither car has an automatic transmission**
- {MM}
- {AA, AM, MA}
- {AM, MA}
- {AM, MA, MM}
- {AA}
**Which of these events are simple events? (Select all that apply.)**
- [ ] B
- [ ] C
- [ ] D
**(d) What outcomes are in the event B and C?**
- {AM, MA}
- {MM}
- {AM, MA, MM}
- {AA, AM, MA}
- {AA}
**What outcomes are in the event B or C?**
- {MM}
- {MM, AM, MA}
- {AM, MA, AA}
- {AA}
- {AM, MA}
This exercise helps to understand the concepts of sample space, events, and outcomes in probability related to the transmission type of purchased cars.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec13ab4f-5933-4c78-80c6-824491a34faa%2F4e5aa14f-fd80-418a-a9fb-c44b00334812%2Fzvgsim_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Transmission Type Outcomes in Probability**
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)?**
- Sample space = {A, M}
- Sample space = {A, M, AA, AM, MA, MM}
- Sample space = {AA, AM, MM}
- Sample space = {AA, AM, MA}
- Sample space = {A, M}
**(b) Display the possible outcomes in a tree diagram.** (Visual representation required; this step encourages drawing a tree diagram on paper.)
**(c) List the outcomes in each of the following events.**
**I. B, the event that at least one car has a manual transmission**
- {AM, MA}
- {AA}
- {MM}
- {AM, MA, AA}
- {MM, AM, MA}
**II. C, the event that exactly one car has an automatic transmission**
- {AA, AM, MA}
- {AA}
- {MM}
- {AM, MA}
- {AM, MA, MM}
**III. D, the event that neither car has an automatic transmission**
- {MM}
- {AA, AM, MA}
- {AM, MA}
- {AM, MA, MM}
- {AA}
**Which of these events are simple events? (Select all that apply.)**
- [ ] B
- [ ] C
- [ ] D
**(d) What outcomes are in the event B and C?**
- {AM, MA}
- {MM}
- {AM, MA, MM}
- {AA, AM, MA}
- {AA}
**What outcomes are in the event B or C?**
- {MM}
- {MM, AM, MA}
- {AM, MA, AA}
- {AA}
- {AM, MA}
This exercise helps to understand the concepts of sample space, events, and outcomes in probability related to the transmission type of purchased cars.
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