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Basic Concepts, Types And Rules Of Probability In Statistics - Key Probability Terms - YouTube
Channel: Whats Up Dude
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Rolling a die, drawing a card out of a deck, and聽
flipping a coin are all things we're familiar聽聽
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with and these are often used to discuss the聽
basic concepts of probability. There are 4聽聽
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key terms that are often used with probability, a聽
probability experiment, which is a process where聽聽
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specific results are obtained, such as rolling聽
a die as there are only six possible outcomes.聽聽
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And outcome is another key term, which is a single聽
result of a probability experiment, so, if you draw聽聽
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a four of hearts from a full deck of cards that聽
is an outcome. Sample space is another key term聽聽
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and it is a set of all possible outcomes for a聽
probability experiment. For instance the sample聽聽
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space for rolling two dice is here, and you can see聽
the possible outcomes for die one and the possible聽聽
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outcomes for die number two, and the sample space聽
is the pairs of numbers listed on the chart聽聽
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here. So there are 36 possible outcomes in this聽
sample space. Event is another key term used in聽聽
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probability and an event is a set of outcomes聽
of a probability experiment, it is a subset of聽聽
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the sample space, and an event with one outcome聽
is a simple event, and a compound event consists聽聽
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of two or more outcomes. For instance the event of聽
rolling a four on a die roll is a simple event, and聽聽
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the event of getting an even number on a die roll聽
is a compound event. There are three main types聽聽
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of probability, classical probability, empirical聽
probability, and subjective probability. Classical聽聽
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probability is used when each outcome in a sample聽
space is equally likely to occur. For instance the聽聽
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sample space for rolling two dice, and each of these聽
outcomes has the same chance to occur. The formula聽聽
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for this is P of E, probability of any event, equals聽
the number of outcomes in event E, divided by the聽聽
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total number of outcomes in the sample space. So聽
the probability of the two dice totaling 5聽聽
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is P of 5 equals, 4 the number of possible聽
combinations the total up to 5, divided by 36,聽聽
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the total number of outcomes in the sample space.聽
Empirical probability is when each outcome is not聽聽
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equally likely to occur and it is based on聽
observations obtained from experiments. For聽聽
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instance let's say you polled 50 people and ask them聽
what their favorite sport is. Using a frequency聽聽
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table, 29 said football, 11 said basketball, 6聽
said baseball, 3 said soccer and 1 said tennis.聽聽
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Now we can compute probabilities for each of the聽
categories. The formula for empirical probability聽聽
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is the probability of event, equals frequency for聽
the class or the event, divided by the total of the聽聽
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frequencies. So the probability of football being聽
a person's favorite sport is 29 divided by 50,聽聽
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which is 0.58, and the probability of tennis being聽
someone's favorite sport is 1 divided by 50, which聽聽
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is 0.02, and you can convert these to percentages聽
by multiplying by 100 to get 58%, and聽聽
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2%. Subjective probability is based on an聽
educated guess or an estimate. For instance if I聽聽
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were to say there was a 73% chance the Yankees聽
win the World Series next year, this is based on聽聽
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my experience and evaluation. And there are 4 key聽
rules to probability. The first is that probability聽聽
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of an event is between 0 and 1, including 0 and 1, and聽
this is written as 0 less than or equal to the聽聽
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probability of an event, less than or equal to 1.聽
And whatever the value of P is, can be written as聽聽
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a fraction or decimal. For instance the probability聽
of getting a head on a coin toss is 0.5, or 1 over 2.聽聽
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Rule number two is that the sum of all possible聽
outcomes in a sample space is 1. So the sample聽聽
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space for a die roll is 1 through 6, with each聽
having a 1 over 6 probability of occurring, add聽聽
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these up, and we get 1. Rule number three is if it聽
is impossible for a given event to occur, so it's聽聽
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not part of the sample space, its probability is聽
zero. For instance the probability of rolling 8聽聽
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on a die roll is not part of the sample space, so聽
its probability is zero. Rule number four is that聽聽
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if an event is certain to occur, its probability聽
is 1. So the probability of rolling a 1 through聽聽
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a 6 on a die roll is certain to happen, so its聽
probability is 1. Alright my friends, hopefully聽聽
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this video helped you out, I do have more videos聽
right there for you, till next time, I am outta here.
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