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Outcomes and Events

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Hi. This tutorial covers outcomes and events. So before we start looking at outcomes and events, I wanted to give us a good working definition of what a chance experiment is. So a chance experiment is any situation where there is uncertainty about which of two or more outcomes will result.

So I have a couple examples of chance experiments. So Example 1, drawing a card from a deck and recording the suit of the cards-- so if we did this chance experiment, here's a deck of cards, well shuffled. I draw a card. There is uncertainty about which suit comes up. So this happened to be diamonds. But I did not know if that was going to be diamonds or a different suit.

Experiment number 2, rolling a die and recording the number shown-- so if I roll the die, I got a two. There was uncertainty about which outcome or which value that the die would show. And example 3, sitting at a stop light and recording the make of the next car that runs a red light. So I'd be sitting there, I wouldn't know what the make of the car would be that runs the red light. It could be a Chevy, it could be a Ford. There's uncertainty there.

Now if you have a chance experiment, we can define something called an outcome. So an outcome is any single result of a chance experiment. An event, then, is a set of one or more outcomes. And a trial is each occurrence of a chance experiment. So let's go back to those examples and figure what would be an outcome, what would be an event, and what would be a trial.

So let's start again with Example 1. So drawing a card from a deck and recording the suit of the card-- so again, if I were to draw this card, the outcome here, since I'm recording the suit, the outcome would be diamonds. So again, the outcome would be diamonds. So if I drew another one, the outcome there would be hearts. So the suit there would be considered the outcome.

Now what an event could be, is an event could be maybe getting a red card. So your event would be getting a red. So here, no, I did not get a red, I got a black card. So that might be considered an event.

Now if we go to rolling a die, if I roll a die, my two is my outcome. A three is an outcome. Now, each time I roll that die, that's considered a different trial. So far, I've done three trials and got three different outcomes.

An event associated with Example 2 might be, well, maybe it would be rolling an odd number. So I got a one, yes, that's an odd number. If I roll that again, four, no, that is not an odd number. So that would be an event there.

And for Example 3, an outcome could be Chevy. Maybe a Chevy was the one that ran a red light. The next one could be Ford, or could be Honda. So those would all be outcomes. And each outcome would be associated with a different trial.

What an event could be for 3 might be, was it an American-made car, or was it a foreign car? So an event could be, let it be a American-made car. So a Ford or a Chevy would meet that event, but a Honda would not.

So now based on outcomes and events, there are always probabilities associated with them. So a probability is a way to numerically express the likelihood of an outcome or an event. So if I'm rolling a die, three. So I knew before I rolled that die that I would have a 1 out of 6 chance of getting a three. So that one out of six or 1/6 would be a probability. So probability value must be between 0 and 1. Values close to zero are very unlikely. Values close to 1 are very likely. Probabilities expressed as percents range from 0% to 100%.

Let's also take a look at one more example that you'll see commonly in the newspaper or on the internet. So the following is a five-day forecast. So we have five days here. And the probabilities that we're looking at here are the probability of a chance of rain. So we can see that for Thursday, there is a 20% chance of rain. So that is a probability there.

So let's go through each of these questions here. So what is the chance experiment associated with these probabilities, so with these chance of rain? So what's the chance experiment? So the chance experiment here is basically observing a day and then deciding if it rains or not.

So the outcomes associated with the chance experiment are either no rain or rain. And then so do are these probabilities represent? So on July 17, so on July 17, there's a 30% chance of rain. So basically, what that means is that out of other days with these same situations, there is a 30% chance-- it rained on 30% of those days.

So in the long run, on days similar to July 17, since 30% of the time there was rain, we would say that there's a 30% probability of it raining on the 17th. So this is just a common time where you see probabilities, and in this case, expressed as a percent.

So that has been your tutorial on outcomes and events. Thanks for watching.