The following figure expresses the content of the definition of the probability of an event:. In ordinary language probabilities are frequently expressed as percentages. Assign a probability to each outcome in the sample space for the experiment that consists of tossing a single fair coin. Assign a probability to each outcome in the sample space for the experiment that consists of tossing a single fair die.
With outcomes labeled according to the number of dots on the top face of the die, the sample space is the set. Two fair coins are tossed. Find the probability that the coins match, i.
The theory of probability does not tell us how to assign probabilities to the outcomes, only what to do with them once they are assigned. The previous three examples illustrate how probabilities can be computed simply by counting when the sample space consists of a finite number of equally likely outcomes. In some situations the individual outcomes of any sample space that represents the experiment are unavoidably unequally likely, in which case probabilities cannot be computed merely by counting, but the computational formula given in the definition of the probability of an event must be used.
A student is randomly selected from this high school. Find the probabilities of the following events:. Different types of sample spaces in probability Ask Question. Asked 4 years ago. Active 3 years, 3 months ago. Viewed 18k times. A sample space can be finite or infinite.
A sample space can be discrete or continuous. A sample space can be countable or uncountable. Which one of the following above is correct? I got confuse because of the following two statements in this text book Discrete Probability Law : If the sample space consists of a finite number of possible outcomes , then the probability law is specified by the probabilities of the events that consist of a single element.
Continuous Models : Probabilistic models with continuous sample spaces differ from their discrete counterparts in that the probabilities of the single-element events may not be sufficient to characterize the probability law.
The second one seems to be the usual definition. Add a comment. Alright laughing. There is a small and then this is a small, this is a small vanilla. This color changing is really, it's a difficult thing. Small vanilla. And all of these, these are all, this would be a medium chocolate.
Medium strawberry. Medium vanilla. Large chocolate, large strawberry, large vanilla. And once again you have nine outcomes. This is another way to think about all of the possible outcomes when you're looking at these two ways in which my cupcakes could vary. Another way, a third way that you could do it, is you could literally just construct a table.
Well you could say, okay I could have a chocolate, actually I'm going to use the letters again. So let's say we make, this is the flavor column. And then this is the size column. Size column. And so you could say I could have a chocolate that is, so let's see, there's three types of chocolate that I could have.
And they could be they could be small, medium, or large. You could say there's three types of, three types of strawberry. It could be small, medium, or large. So let me write that in. Small, medium, large. Or you could say oh, there's three types of vanilla. There's three types of, I'm color changing again. Three types of vanilla. Once again, it could be small, medium, or large. So you have these nine possibilities. Now, sample space, the sample space isn't telling you if they're equally likely or not.
It's just telling you, hey, if you're gonna do an experiment, what are all the different possibilities, the possible outcomes for that experiment? Now in the case where they are equally likely, it can be very, very useful because you can say you could do something like, if you said okay, it's equally likely to pick any one of these nine outcomes, you could say well what's the probability of, what's the probability of getting something that is either small or chocolate?
And so you could see well how many of those events out of the total actually meet that constraint? But we'll do more of that in future videos. That's just a little bit of a clue of why we even care about things like sample spaces.
We could also write out the sample space for rolling two dice, but to simplify things mathematicians often use sample space diagrams. Look at this sample space diagram for rolling two dice:. From the diagram, we can see that there are 36 possible outcomes.
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