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## Precalculus and College Algebra - Full Course for Beginners

Learn Precalculus and College Algebra in this course for beginners. Over these next few Precalculus videos you will be 100% prepared to learn Calculus. I have found that most people think Calculus is difficult because they don't know everything required to easily learn it. This tutorial series will solve that.

In this video I'll teach how to :

► Solve Linear Equations
► Find the Slope of a Line
► Graph Complex Equations
► Convert to Standard Form
► Find Least Common Multiple
► Create Equations from a Slope & Point
► Find Distance between Points
► Find Greatest Common Factor
► Solve Inequalities
► Graph Inequalities
► And more

## Precalculus and College Algebra 9: Logarithm Equations

#precalculus #collegealgebra #calculus

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## Precalculus Course: Addition Rule for Probability

In this Precalculus Course's video, we will learn the Addition rule for probability. Venn diagrams and the addition rule for probability

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## Precalculus Course: Probability with Playing Cards and Venn Diagrams

In this Precalculus Course's video, we will learn the Probability with playing cards and Venn diagrams. Probability of compound events. The Addition Rule. Common Core Standard 457 S-CP.7

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## Precalculus Course: Statistical Significance Of Experiment

In this Precalculus Course's video, we will learn the Statistical significance of experiment

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## Precalculus Course: Random Numbers for Experimental Probability

In this Precalculus Course's video, we will learn the Using a list of random number to calculate an experimental probability.

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## Precalculus Course: Random Number List to Run Experiment

In this Precalculus Course's video, we will learn how to Using a list of random numbers to simulate multiple trials of an experiment.

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## Precalculus Course: Experimental Versus Theoretical Probability Simula

In this Precalculus Course's video, we will learn the  Experimental versus theoretical probability simulation.

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## Precalculus Course: Comparing Theoretical to Experimental Probabilites

Compare expected probabilities to what really happens when we run experiments.

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## Precalculus Course: Bringing The Set Operations Together

Sal summarizes the set operations that he has discussed in the previous videos.

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## Precalculus Course: Subset, Strict Subset, and Superset

Sal explains the difference between a subset, a strict subset, and a superset. He also explains the notation behind these ideas.

Let's define ourselves some sets. So let's say the set A is composed of the numbers 1. 3. 5, 7, and 18. Let's say that the set B-- let me do this in a different color-- let's say that the set B is composed of 1, 7, and 18. And let's say that the set C is composed of 18, 7, 1, and 19. Now what I want to start thinking about in this video is the notion of a subset. So the first question is, is B a subset of A? And there you might say, well, what does subset mean? Well, you're a subset if every member of your set is also a member of the other set. So we actually can write that B is a subset-- and this is a notation right over here, this is a subset-- B is a subset of A. B is a subset. So let me write that down. B is subset of A. Every element in B is a member of A. Now we can go even further. We can say that B is a strict subset of A, because B is a subset of A, but it does not equal A, which means that there are things in A that are not in B. So we could even go further and we could say that B is a strict or sometimes said a proper subset of A. And the way you do that is, you could almost imagine that this is kind of a less than or equal sign, and then you kind of cross out this equal part of the less than or equal sign. So this means a strict subset, which means everything that is in B is a member A, but everything that's in A is not a member of B. So let me write this. This is B. B is a strict or proper subset. So, for example, we can write that A is a subset of A. In fact, every set is a subset of itself, because every one of its members is a member of A. We cannot write that A is a strict subset of A. This right over here is false. So let's give ourselves a little bit more practice. Can we write that B is a subset of C? Well, let's see. C contains a 1, it contains a 7, it contains an 18. So every member of B is indeed a member C. So this right over here is true. Now, can we write that C is a subset? Can we write that C is a subset of A? Can we write C is a subset of A? Let's see. Every element of C needs to be in A. So A has an 18, it has a 7, it has a 1. But it does not have a 19. So once again, this right over here is false. Now we could have also added-- we could write B is a subset of C. Or we could even write that B is a strict subset of C. Now, we could also reverse the way we write this. And then we're really just talking about supersets. So we could reverse this notation, and we could say that A is a superset of B, and this is just another way of saying that B is a subset of A. But the way you could think about this is, A contains every element that is in B. And it might contain more. It might contain exactly every element. So you can kind of view this as you kind of have the equals symbol there. If you were to view this as greater than or equal. They're note quite exactly the same thing. But we know already that we could also write that A is a strict superset of B, which means that A contains everything B has and then some. A is not equivalent to B. So hopefully this familiarizes you with the notions of subsets and supersets and strict subsets.

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## Precalculus Course: Universal Set and Absolute Complement

Sal moves onto more challenging set ideas and notation like the universal set and absolute complement.

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## Precalculus Course: Relative Complement Or Difference Between Sets

In this Precalculus Course's video, we will learn the Relative Complement Or Difference Between Sets. Sal shows an example finding the relative complement or difference of two sets A and B.

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## Precalculus Course: Intersection and Union Of Sets

Sal shows examples of intersection and union of sets and introduces some set notation.

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## Precalculus Course: Describing Subsets Of Sample Spaces Exercise

In this example, determine the scenarios that are probable given the rolling of two dice.

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## Precalculus Course: Die Rolling Probability

We're thinking about the probability of rolling doubles on a pair of dice. Let's create a grid of all possible outcomes.

Find the probability of rolling doubles on two six-sided dice numbered from 1 to 6. So when they're talking about rolling doubles, they're just saying, if I roll the two dice, I get the same number on the top of both. So, for example, a 1 and a 1, that's doubles. A 2 and a 2, that is doubles. A 3 and a 3, a 4 and a 4, a 5 and a 5, a 6 and a 6, all of those are instances of doubles. So the event in question is rolling doubles on two six-sided dice numbered from 1 to 6. So let's think about all of the possible outcomes. Or another way to think about it, let's think about the sample space here. So what can we roll on the first die. So let me write this as die number 1. What are the possible rolls? Well, they're numbered from 1 to 6. It's a six-sided die, so I can get a 1, a 2, a 3, a 4, a 5, or a 6. Now let's think about the second die, so die number 2. Well, exact same thing. I could get a 1, a 2, a 3, a 4, a 5, or a 6. Now, given these possible outcomes for each of the die, we can now think of the outcomes for both die. So, for example, in this-- let me draw a grid here just to make it a little bit neater. So let me draw a line there and then a line right over there. Let me draw actually several of these, just so that we could really do this a little bit clearer. So let me draw a full grid. All right. And then let me draw the vertical lines, only a few more left. There we go. Now, all of this top row, these are the outcomes where I roll a 1 on the first die. So I roll a 1 on the first die. These are all of those outcomes. And this would be I run a 1 on the second die, but I'll fill that in later. These are all of the outcomes where I roll a 2 on the first die. This is where I roll a 3 on the first die. 4-- I think you get the idea-- on the first die. And then a 5 on the first to die. And then finally, this last row is all the outcomes where I roll a 6 on the first die. Now, we can go through the columns, and this first column is where we roll a 1 on the second die. This is where we roll a 2 on the second die. So let's draw that out, write it out, and fill in the chart. Here's where we roll a 3 on the second die. This is a comma that I'm doing between the two numbers. Here is where we have a 4. And then here is where we roll a 5 on the second die, just filling this in. This last column is where we roll a 6 on the second die. Now, every one of these represents a possible outcome. This outcome is where we roll a 1 on the first die and a 1 on the second die. This outcome is where we roll a 3 on the first die, a 2 on the second die. This outcome is where we roll a 4 on the first die and a 5 on the second die. And you can see here, there are 36 possible outcomes, 6 times 6 possible outcomes. Now, with this out of the way, how many of these outcomes satisfy our criteria of rolling doubles on two six-sided dice? How many of these outcomes are essentially described by our event? Well, we see them right here. Doubles, well, that's rolling a 1 and 1, that's a 2 and a 2, a 3 and a 3, a 4 and a 4, a 5 and a 5, and a 6 and a 6. So we have 1, 2, 3, 4, 5, 6 events satisfy this event, or are the outcomes that are consistent with this event. Now given that, let's answer our question. What is the probability of rolling doubles on two six-sided die numbered from 1 to 6? Well, the probability is going to be equal to the number of outcomes that satisfy our criteria, or the number of outcomes for this event, which are 6-- we just figured that out-- over the total-- I want to do that pink color-- number of outcomes, over the size of our sample space. So this right over here, we have 36 total outcomes. So we have 36 outcomes, and if you simplify this, 6/36 is the same thing as 1/6. So the probability of rolling doubles on two six-sided dice numbered from 1 to 6 is 1/6.

#precalculus