Mẹo Hướng dẫn List down the sample space or all the possible outcomes of the following experiment Chi Tiết
An Sơn Hà đang tìm kiếm từ khóa List down the sample space or all the possible outcomes of the following experiment được Update vào lúc : 2022-11-21 03:44:04 . Với phương châm chia sẻ Kinh Nghiệm về trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi đọc nội dung bài viết vẫn ko hiểu thì hoàn toàn có thể lại phản hồi ở cuối bài để Tác giả lý giải và hướng dẫn lại nha.A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment. If it contains a finite number of outcomes, then it is known as discrete or finite sample spaces.
Nội dung chính Show- Tossing a CoinTossing Two CoinsA Die is ThrownTwo Dice are ThrownSample ProblemSample SpaceWhat are the possible outcomes and sample space of the experiment?What is the sample space of all possible outcomes?What is a list of all possible outcomes of an experiment called?What is the sample space of the experiment example?
The samples spaces for a random experiment is written within curly braces “ “. There is a difference between the sample space and the events. For rolling a die, we will get the sample space, S as 1, 2, 3, 4, 5, 6 whereas the sự kiện can be written as 1, 3, 5 which represents the set of odd numbers and 2, 4, 6 which represents the set of even numbers. The outcomes of an experiment are random and the sample space becomes the universal set for some particular experiments. Some of the examples are as follows:
Tossing a Coin
When flipping a coin, two outcomes are possible, such as head and tail. Therefore the sample space for this experiment is given as
Sample Space, S = H, T = Head, Tail
Tossing Two Coins
When flipping two coins, the number of possible outcomes are four. Let, H1 and T1 be the head and tail of the first coin and H2 and T2 be the head and tail of the second coin respectively and the sample space can be written as
Sample Space, S = (H1, H2), (H1, T2), (T1, H2), (T1, T2)
In general, if you have “n” coins, then the possible number of outcomes will be 2n.
Example: If you toss 3 coins, “n” is taken as 3.
Therefore, the possible number of outcomes will be 23 = 8 outcomes
Sample space for tossing three coins is written as
Sample space S = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
A Die is Thrown
When a single die is thrown, it has 6 outcomes since it has 6 faces. Therefore, the sample is given as
S = 1, 2, 3, 4, 5, 6
Two Dice are Thrown
When two dice are thrown together, we will get 36 pairs of possible outcomes. Each face of the first die can fall with all the six faces of the second die. As there are 6 x 6 possible pairs, it becomes 36 outcomes. The 36 outcome pairs are written as:
(beginarraylbeginBmatrix (1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6) \ (2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6) \ (3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\ (4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6) \ (5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6) \ (6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6) endBmatrixendarray )
If three dice are thrown, it should have the possible outcomes of 216 where n in the experiment is taken as 3, so it becomes 63 = 216.
Sample Problem
Question:
Write the sample space for the given interval [3,9].
Solution:
Given interval: [3, 9]
As the integers given are in the closed interval, we can take the value from 3 to 9.
Therefore, the sample space for the given interval is:
Sample space = 3, 4, 5, 6, 7, 8, 9
Stay tuned with BYJU’S – The Learning App for more such information on probability, and also watch other maths-related videos.
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The following diagram shows how the sample space for an experiment can be represented by a list, a table, and a tree diagram. Scroll down the page for examples and solutions.
Sample Space
In the study of probability, an experiment is a process or investigation from which results are observed or recorded.
An outcome is a possible result of an experiment.
A sample space is the set of all possible outcomes in the experiment. It is usually denoted by the letter S. Sample space can be written using the set notation, .
Experiment 1: Tossing a coin
Possible outcomes are head or tail.
Sample space, S = head, tail
Experiment 2: Tossing a die
Possible outcomes are the numbers 1, 2, 3, 4, 5, and 6
Sample space, S = 1, 2, 3, 4, 5, 6
Experiment 3: Picking a card
In an experiment, a card is picked from a stack of six cards, which spell the word PASCAL.
Possible
outcomes are P, A 1, S, C, A 2 and L.
Sample space, S = P, A 1, S, C, A 2 L. There are 2 cards with the letter ‘A’
Experiment 4: Picking 2 marbles, one a time, from a bag that contains many blue and red marbles.
Possible outcomes are: (Blue, Blue), (Blue, Red), (Red, Blue) and (Red, Red).
Sample space, S = (B,B), (B,R), (R,B), (R,R).
A simple explanation of Sample Spaces for Probability
- Show Video Lesson
[embed]https://www.youtube.com/watch?v=O9l7TEzxZl8[/embed]
Sample Space Of An Event
Sample space is all the possible outcomes of an sự kiện. Sometimes the sample space is easy to determine. For example, if you roll a dice, 6 things could happen. You could roll a 1, 2, 3, 4, 5, or 6.
Sometimes sample space is more difficult to determine, so you can make a tree diagram or a list to help you figure out all the possible outcomes.
Example 1:
You are ordering pizza. You can choose a small, medium or large pizza and you can choose cheese or pepperoni. What are the possible ways that you could could
order a pizza? How many combinations could you have?
Example 2:
Daisy has 3 pairs of shorts, 2 pairs of shoes and 5 t-shirts. How many outfits can she make?
- Show Video Lesson
[embed]https://www.youtube.com/watch?v=BLGlB4MZEPY[/embed]
This lesson is on finding simple probabilities and sample spaces.
Example:
When you roll a die,
Example:
Use the spinner below to answer the following questions:
- Show Video Lesson
[embed]https://www.youtube.com/watch?v=hptglL-vgqY[/embed]
The following video explains simple probability, experiments, outcomes, sample space and probability of an sự kiện. It also gives an example of a simple probability problem.
Example:
A jar contains five balls that are numbered 1 to 5. Also, two of the balls are yellow and the others are red. They are numbered and colored as shown below.
- Show Video Lesson
[embed]https://www.youtube.com/watch?v=c3M99TQRuq8[/embed]
Lists and Sample Spaces - Probability
Example:
Entrees - Ribs, Chicken
Sides - Mac and Cheese, Veggies,
Mashed Potatoes
Drinks - Water, Coffee, Milk
What are the different possibilities for the menu?
- Show Video Lesson
[embed]https://www.youtube.com/watch?v=Su29BCpPwSE[/embed]
Explains three methods for listing the sample space of an sự kiện and introduces conditional probability: List, Table, Tree Diagram.
- Show Video Lesson
[embed]https://www.youtube.com/watch?v=x-wduLmn2ZY[/embed]
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What are the possible outcomes and sample space of the experiment?
The sample space of a random experiment is the collection of all possible outcomes. An sự kiện associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1.What is the sample space of all possible outcomes?
The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive (i.e., they cannot occur simultaneously).What is a list of all possible outcomes of an experiment called?
A set of all possible outcomes of an experiment is called a sample space.What is the sample space of the experiment example?
The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set. Here are some examples of random experiments and their sample spaces: Random experiment: toss a coin; sample space: S=heads,tails or as we usually write it, H,T. Tải thêm tài liệu liên quan đến nội dung bài viết List down the sample space or all the possible outcomes of the following experiment