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Outcomes and Events

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In this tutorial, you're going to understand the differences and similarities between outcomes and events, and we'll delve into probability theory as well. So, in probability, we define an outcome as the singular result of some random process, so it's-- when you roll a die, it's the role of a one, or the rolling of a six. There's only one, singular result.

So, let's talk about some examples. Suppose the random process that we're talking about is die rolling, and rolling a five would be considered an outcome. Suppose the random process we're talking about is flipping a coin. Tails could be an outcome. And suppose that the random process we're talking about is spinning the wheel on the Wheel of Fortune. Bankrupt would be considered one of our outcomes because that's one of the sectors on the wheel.

Now, there's a difference between outcomes and events. While outcomes only have one result, events can have multiple results. So, for instance, in rolling a die, while an outcome would be a five, an event could be rolling an even number. That consists of the outcomes two, four, and six.

Now, it could be that an event has one outcome in it, like with the coin flipping. Maybe the coin flipping-- an outcome would be tails, but maybe tails is also considered an event. This is an event with one outcome in it. And finally, on the Wheel of Fortune example, maybe a sector over $500-- there are several of them.

Now, probability is going to be defined as the likelihood of a particular event occurring when you do one version of a random process. Now, when you do the random process once, like spinning a wheel, or rolling a die, or flipping a coin, that's called a trial. Doing it once is called one trial.

And probability is a number between 0 and 1, with the numbers closer to zero than one being classified as unlikely. And the numbers that are closer to one than zero are classified as likely. The number right here in between, which is 0.5, is considered neither likely nor unlikely. It's equally likely to occur as not occur.

So, an example of this would be flipping a coin-- flipping tails on the coin. There's just as many ways to get tails as not get tails, and so we're going to say that that numerically has a probability of one-half.

There are some other unlikely events, like drawing a face card from a deck of cards. There are fewer face cards than non-face cards, which means that it would be unlikely to pick a face card.

And if you want something really unlikely, you could play the lottery. Winning the lottery has a very low probability-- almost zero. A zero probability indicates that the event is impossible. It could not happen. Winning the lottery is almost impossible.

Now, onto likely events. Suppose you are selecting a letter at random from the alphabet. It's more likely that you would select a constant than a vowel. And if you want something with a really high probability, like one, you could talk about rolling a six or less on a die. A probability of one indicates that the event is certain to happen. And in this case, rolling six or less on a die has to happen. The die result has to be the number six or less than that.

And so, to recap, probability is a way to quantify likelihood. It's a way to determine how likely certain outcomes or sets of outcomes, called events, are when you run a trial of a chance experiment. One outcome is the singular result of one trial, whereas an event could be many outcomes, many results, of a single trial.

So we talked about outcomes, events, trials, and probability, which is numerical likelihood.

Good luck, and we'll see you next time.