Concepts of sample space, sample points and events

Luc Zio
A free video tutorial from Luc Zio
Adjunct faculty of Statistics, Data Scientist
4.4 instructor rating • 7 courses • 3,225 students

Lecture description

In this lecture, we cover detailed explanations about the concept of a sample space in probability, sample points and events. These concepts are essential for solving probability problems.

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Learn Probability concepts and counting techniques

Learn how to solve probability and counting problems through this hands-on course with many quizzes and solved problems.

02:50:57 of on-demand video • Updated October 2013

  • By the end of this course you will understand probability concepts and be able to solve commons probability problems
  • By the end of this course, you will be able to compute conditional probabilities
  • By the end of this course, you will be able to understand how to solve probability problems using the addition and multiplicative rules.
  • By the end of this course, you will be able to solve basic counting problems using permutations and combinations formulas
  • By the end of this course, you will be able to compute probabilities using the Poisson distribution
  • By the end of this course, you will be able to compute probabilities using the Binomial distribution
  • By the end of this course you will understand how to solve problems using the Hypergeometric distribution
  • By the end of this course, you will be able to compute probabilities using the multinomial distribution
  • By the end of this course, you will be able to compute probabilities using the Geometric and Negative Binomial (or Pascal) distribution
English [Auto] Introductory statistics course not probability counting technique and discrete probability distribution. What is probability. It is the systematic study of uncertainty. It's also defined as the likely will or chance that something will happen. Another definition is that a measure of the degree of belief that an event will Ah-Q probability allows us to make the inferential jump from sample to population and to give a measure of really ability of estimate. All right but is that die. So a device that has six faces is one having the same chance of coming up. We say that the die the faces of the day are equally likely. So the chance of getting a tree is the same as the chance of getting a 5 or 6 1 or 2 and under that. Now when we roll two dice is the plural is Dyce's we roll two dices we get 286 outcome we will show how the 36 outcome or Ted. All right. We're continuing on with the basic notion and definition we stuck with the concept of an experiment. An experiment is an option or trial that leads to a single outcome that cannot be predicted with certainty. So example of experiment tossing a coin rolling a die etc.. Selecting a card from a deck of 52 cards does an experiment. The result of an experiment is called an observation outcome or a sample point all possible outcome of an experiment call sample. When a sample space is the collection of all the sample and even is a specific collection of sample. So we will see how in practical terms these definition work what today is best. Anderson the definition of best on this two two problems. All right basic notion and definition continue. A sample space is a collection of all the sample plan or outcome. So here for example we all die once the sample space will consist of all the elements we can get which will be 1 2 3 4 5 6. These are the sample. Each one of them is a sample of one and the sample space is the collection of all the samples that we can get. When the dies Oren's right we toss the plane once does that the sample point ahead as a sample point until there's a sample point. Now the sample space is the collection of all of them. So in Brace's we put all the element of the sample space. The coin toss twice the sample space will consist of this element. Had had had tell tale had telltale finally the coin toss to return the sample space which consists of all these elements. So like the first one will be head head head meaning that we often add in all the Tweed tosses. The second one had had tilt means that in the first two tosses we got heads but in the third one we got to tell and so forth until we got Tell-Tale to concept of probability events. OK suppose that the dice were all dead even if we define us top 10 and even number. Again we said that the event is a specific collection of sample point. So here we find that to be obtaining and even numbers. So the event would have the sample point to 4 6. These are even numbers. So as you can see this event is a subset of the sample space. Now let's consider another experiment where the coin is tossed 3 times and we find that even the two to be obtained at most one had at most one had means obtaining had been up to one had no more. So the event B will consist of the element T T T. So in here we obtains your head and not you one had one had won. So these that the element of the event be tween diagram of the toss of a coin three times. So when we toss the coin three times often we are asked to write down the sample space. The quickest way to reading the sample space down is building the tree diagram and let's go over with that to be sure. Here in the first US we had head or tail as it. The second toss we could have you had tail had tail so we keep on building the tree to toss her tail. Had to then we stop here because we toss the queen retired. Once we do that we follow the tree top10 the sample point. So here we had had had had had had had had tail had tail had had to tell and so forth until we write down all sample space of what day being rolled twice. So when we rolled the dice twice we will have this situation. First time second time at the intersection we have the sample point. So 1:01 mean that we got one on the first row and one on the second and so forth. They will be in total to six sample point. Thank you.