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Refer to Exercise 3.33. Use the same event definitions to
Chapter 3, Problem 34E(choose chapter or problem)
Problem 34E
Refer to Exercise 3.33. Use the same event definitions to do the following exercises.
a. Write the event that the outcome is “On” and “High” as an intersection of two events.
b. Write the event that the outcome is “Low” or “Medium” as the complement of an event.
3.33 The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities associated with each of the six possible outcome pairs are given in the accompanying two-way table.
Low |
Medium |
High |
|
On |
.50 |
.10 |
.05 |
Off |
.25 |
.07 |
.03 |
Consider the following events:
A: {On}
B: {Medium or On}
C: {Off and Low}
D: {High}
a. Find P(A).
b. Find P(B).
c. Find P(C).
d. Find P(D).
e. Find P(Ac).
f. Find P(A ∪ B).
g. Find P(A ∩ C).
h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.
Questions & Answers
QUESTION:
Problem 34E
Refer to Exercise 3.33. Use the same event definitions to do the following exercises.
a. Write the event that the outcome is “On” and “High” as an intersection of two events.
b. Write the event that the outcome is “Low” or “Medium” as the complement of an event.
3.33 The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities associated with each of the six possible outcome pairs are given in the accompanying two-way table.
Low |
Medium |
High |
|
On |
.50 |
.10 |
.05 |
Off |
.25 |
.07 |
.03 |
Consider the following events:
A: {On}
B: {Medium or On}
C: {Off and Low}
D: {High}
a. Find P(A).
b. Find P(B).
c. Find P(C).
d. Find P(D).
e. Find P(Ac).
f. Find P(A ∪ B).
g. Find P(A ∩ C).
h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.
ANSWER:
Solution:
Step 1 of 2:
The outcomes of two variables are (Low, Medium, high) and (On, Off), respectively.
The events are defined as:
A: {On}
B: { Medium or On}
C: { Off and Low}
D: { High}
- We have to write that the outcome is “On” and “High” as an intersection of two events.
- We have to write that the outcome is “Low” or “Medium” as the complement of an event.