Question
Гry These:
Show your answers. (
A die is rolled.
. List all the outcomes
2. List all the sample space
3. List all the events
Show your answers. (
A die is rolled.
. List all the outcomes
2. List all the sample space
3. List all the events
Ask by Wang Summers. in the Philippines
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Outcomes: 1, 2, 3, 4, 5, 6
Sample Space: {1, 2, 3, 4, 5, 6}
Events:
- Rolling a 3: {3}
- Rolling an even number: {2, 4, 6}
- Rolling a number greater than 4: {5, 6}
- Rolling a number less than or equal to 3: {1, 2, 3}
- Rolling a 6: {6}
- Rolling a number not 6: {1, 2, 3, 4, 5}
- Rolling a certain event: {1, 2, 3, 4, 5, 6}
- Rolling an impossible event: {}
Solution
Certainly! Let’s tackle each part of the problem step by step.
1. List All the Outcomes
When you roll a standard six-sided die, each face represents a possible outcome. The outcomes are the numbers that can appear on the top face of the die after a roll.
Outcomes:
- 1
- 2
- 3
- 4
- 5
- 6
2. List the Sample Space
The sample space is a comprehensive set that includes all possible outcomes of a random experiment. In this case, the experiment is rolling a die.
Sample Space (S):
3. List All the Events
An event is any subset of the sample space. This means it can consist of one outcome, multiple outcomes, or even no outcomes at all. Since the sample space has 6 outcomes, there are
a. Single Outcome Events (Simple Events):
These events consist of exactly one outcome.
-
Event A: Rolling a 3
-
Event B: Rolling a 5
b. Multiple Outcome Events:
These events consist of two or more outcomes.
-
Event C: Rolling an even number
-
Event D: Rolling an odd number
-
Event E: Rolling a number greater than 4
-
Event F: Rolling a number less than or equal to 3
c. Complementary Events:
These are pairs of events where one event is the complement of the other.
-
Event G: Rolling a number that is not 6
-
Event H: Rolling a 6
(Here, Event G is the complement of Event H, and together they cover the entire sample space.)
d. Impossible and Certain Events:
-
Impossible Event: An event that cannot occur.
-
Certain Event: An event that is always true.
Summary
- Outcomes: 1, 2, 3, 4, 5, 6
- Sample Space:
- Events: Any subset of the sample space, including examples like rolling an even number ({2, 4, 6}), rolling a 3 ({3}), rolling greater than 4 ({5, 6}), etc.
Understanding these basics will help you analyze probabilities and comprehend how different events relate to one another within the sample space.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
Когда вы бросаете стандартный игральный кубик, он может приземлиться на одну из шести граней. Каждая грань имеет одну из чисел от 1 до 6. Таким образом, возможные исходы – это: 1, 2, 3, 4, 5, 6. Эти числа представляют все результаты, которые вы можете получить при броске.
Образец пространства включает в себя все возможные исходы, которые могут произойти. В данном случае это будет набор всех исходов, то есть: S = {1, 2, 3, 4, 5, 6}. Каждое число в этом множестве представляет отдельный исход, который может произойти при броске кубика.
События – это подмножества пространства образца. Например, одно событие может быть “выпало четное число”, что можно представить как A = {2, 4, 6}. Другие примеры событий могут включать “выпало число больше 4” (B = {5, 6}) или “выпало число меньше или равно 3” (C = {1, 2, 3}).
