WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over how to find probability of an event not occurring.
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We have gone over how to find the probability of an event occurring.
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That would be the desired outcome over the total possible outcomes; it is a ratio.
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We are comparing what we are looking for, the desired outcome,
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over how many total possible outcomes there are, what is the total number.
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This ratio is in the form of a fraction, top number over bottom number.
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Probability can also be in the form of a decimal and a percent.
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If I have probability of an event occurring, let's say it is 1/4.
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That is a probability.
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I can change this into a decimal and into a percent.
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Let's just review over that.
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To change this fraction to a decimal, I am going to take the top number and divide it to the bottom number.
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This top number is going to go inside; the 4 on the outside.
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Here I am going to add a decimal point.
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I can always add a decimal point at the end of a number.
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Then I can add 0s.
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I can add 0s as long as it is behind the decimal point and at the end of the number.
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Bring this decimal point up; 4 does not go into 1.
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I am going to use one 0 to make 10.
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4 goes into 10 twice; that is going to give me 8.
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I am going to subtract the 10 with the 8; I get 2.
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I can add another 0; bring that 0 down.
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4 goes into 20 five times; that is going to give you 20.
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Subtract it; I get 0; 1/4 is the same as 0.25.
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You can also think of it as 1 out of 4... let's say I have 4 quarters.
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1 out of the 4 quarters gives me 25 cents.
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To change this to a percent, I take the decimal point.
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I always move it to the right two spaces.
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Think of the decimal as being small and a percent as getting larger.
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Percents are bigger than decimals.
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We have to move it to the right to make the number bigger.
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I am going to move it to the right two spaces.
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The decimal point is now going to be behind the 5.
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Add the percent sign; that is how you change it from decimal to percent.
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Three ways we can write probability; that is the probability of an event occurring.
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To find the probability of an event not occurring is actually going to be 1 minus that number.
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1, why 1?--1 is actually the biggest number we can get for probability.
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It is like seeing the whole thing.
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Say I have a bag of marbles.
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In this bag of marbles, I have let's say 4 red marbles.
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If I want to find the probability of picking a red marble,
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probability of my event will be... I am picking a red.
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How many red marbles do I have?--I have 4.
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My desired outcome is 4 out of... how many total marbles do I have?--4.
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4/4 simplifies to get 1; 1 represents the whole thing; it represents all of it.
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The probability of something happening is 1.
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That means it is 100 percent chance that it is going to happen.
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That is why when you look for the probability of an event not occurring,
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it is as if you are going to take that 1, the whole thing, and you are going to find the leftovers.
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Back to the bag of marbles, let's say I add 2 blues.
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I want to find the probability of picking a red.
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I still have 4 red out of... the total number of marbles changed.
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I now have 6 marbles.
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Here my probability is... I can simplify this; divide each of these by 2.
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I get 2/3; that is the probability of the red.
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I want to find the probability of it not being red, the event not occurring.
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The probability of not red, I am going to take the whole thing which is 1.
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Subtract it from the event occurring, 2/3; it is like finding the leftovers.
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From the whole thing, if I take away this much
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which is the actual probability of the event occurring,
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then it is like I am finding what is left over.
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Here in order to subtract this, I need to make this the same denominator with this.
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I can turn 1 whole into, as long as my top number and bottom number are the same, it is still 1.
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3/3 minus 2/3.
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I made is 3/3 because I want this denominator to be 3,
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the same, for me to be able to subtract these fractions.
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This becomes 1/3.
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Another way to explain this, the probability of picking a red is 2/3.
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The probability of not picking a red is all the rest of it which is 1/3.
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Together the probability, it is either red or not red.
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It is either going to be red or it is not red.
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It is one of those two.
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This is the probability of picking a red.
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This is the probability of picking one that is not red.
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Together they make up the whole thing because it is going to be one or the other.
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The whole thing is just 1; the probability of this not occurring is 1/3.
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The first example, we are going to use a spinner.
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We want to find the probability of spinning or landing on a color that is not green.
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We can do this two ways.
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When we have something like this spinner or maybe a bag of marbles, it is a little bit easier.
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We can make all the colors that are not green our desired outcome.
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I can look for all of the colors that are not green.
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I have 1, 2, 3, 4; 4 that are not green.
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My desired outcome again is not green.
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There is 4 of them; over total of 5.
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The probability of not green will be 4/5.
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The way we did it before, previous slide, it is like
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finding the probability of actually having green and subtracting that from 1.
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We can find the probability of green, subtract it from 1.
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We are still going to get the same answer.
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Here probability of picking a green, that is 1 green out of 5.
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This will be 1 minus 1/5.
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I can change this whole number into 5/5 to make the denominators the same.
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5/5 minus 1/5; 5 minus 1 is 4; over... keep the denominator the same.
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I am going to get the same answer.
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This is obviously the easier way to do it.
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If you can do it this way, then that is fine.
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But you still have to understand that 1 whole would be the whole thing.
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There is 1, 2, 3, 4, 5 out of 5; that would be 1 whole.
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To find the probability of something not occurring would be taking the whole thing
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and subtracting it by the actual probability of the event occurring.
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This next one here, the probability of not red or orange.
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Again we can just make this all the colors that are not red or orange be the desired outcome.
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How many are not red or orange?--here is red; here is orange.
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How many are not either of these?--I have 3.
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My desired outcome would be all the colors that are not red or orange.
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That is going to be my top number; that is 3; over total of 5.
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That would be my answer.
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But again we still have to understand that I can find the probability
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of the red or orange and then take the whole thing, subtract it.
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How many are red or orange?--I have 1, 2; 2 out of 5.
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1 minus 2/5; again change this to 5/5 minus 2/5.
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That is going to give me 3/5.
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Given the probability of an event occurring, find the probability that the event will not occur.
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Here probability of event A occurring is 1/4.
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The probability of the event not occurring is 1 minus this number.
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It is going to be 1 minus 1/4.
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Again change this whole number; it is 1.
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Top number and the bottom number has to be the same because I want to change this to a fraction.
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The denominator has to be a 4; it will be 4/4 minus 1/4.
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Again I made it 4/4 because it has to stay a 1 and the denominator has to be the same.
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This is 4 minus 1 is 3 over 4.
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If the probability of an event occurring is 1/4, then the probability of the event not occurring is 3/4.
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It is like if 1 is the whole thing... 1/4, let's talk money.
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1/4, 1 quarter out of 4 quarters.
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If you use 1 quarter, how many quarters do you have left?
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The remaining of it is 3 quarters; you have 3 left.
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1/4 left over is 3/4; the rest of it is 3/4.
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That is the probability of it not occurring.
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Here 0.67, again 1 minus the probability of B occurring would be 1 minus 0.67.
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Again if this is a dollar minus 67 cents, what do you have left?
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To subtract decimals, I am going to do 1.00.
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I am just turning this 1 into 1.00 because when you subtract decimals, you have to line up the decimal point.
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It is going to be 1.00.
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Again I added 0s because it is at the end of a number behind the decimal point.
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Minus 0.67; this 0, I am going to change to a 10.
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I borrowed it from this; that became a 9; this becomes 0.
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It is 10 minus 7 is 3; 9 minus 6 is 3; nothing there.
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Bring down the decimal point.
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The probability of this not occurring is 0.33.
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For this one, the probability of event C happening is 42 percent.
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The chance of this occurring is 42 percent.
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What is the chance of it not occurring?
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This is a little bit different because it is a percent.
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The whole thing in a percent would be 100 percent.
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If you have a percent, then you would have to do 100 percent minus the 42 percent.
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Or you can think of it as still 1 minus probability of C occurring.
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Then since it is a percent, now we can change it here.
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100 percent, we are changing this 1 whole into a percent.
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Again decimal point at the end; move it two spaces over.
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That is 100 percent minus 42 percent; 100 minus 42 is 58 percent.
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The third example here, the probability of Susie passing the math test is 85 percent.
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Find the probability of her failing the test.
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The probability of an event occurring, which is her passing the math test, is 85 percent.
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We have to find the probability of her failing the test.
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It is out of a possible 100 percent.
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We know that from 100 percent, we have to subtract
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the percent of the probability that she is going to pass the test
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to see what the probability of her failing the test is going to be.
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From here, this is 15 percent.
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This and this together have to make up the 100 percent because that is the whole thing.
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She is either going to pass it; or she is going to fail it.
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This is the pass; this is the fail.
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Together they have to make up the 100 percent, the whole thing.
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Probability of her failing the test is going to be at 15 percent.
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The second one, the probability of Sam not picking the correct colored marble from a bag is 5/8.
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Find the probability of him picking the correct marble.
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The probability of Sam picking the marble, let's just say marble, the correct marble.
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This is what they are asking for.
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They want to know what the probability of him picking the correct marble is going to be.
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He is either going to pick the correct marble or he is going to pick the incorrect marble.
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The probability, what is given to us, of not picking the correct color is going to be 5/8.
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The probability of not picking the correct marble, not correct marble, is 5/8.
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To find the probability of actually picking the correct marble
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is going to be 1 whole because the whole thing is 1 whole.
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There is 8 marbles total; 8/8 is 1; 1 whole; minus 5/8.
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Here to do this, 1 minus 5/8, I need to change this 1 into a whole number.
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Again remember it is 8/8 because I need the denominators to be the same.
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I have to have the top number and the bottom number be the same number for it to just be 1.
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The denominators have to be the same; it has to be 8/8 minus 5/8.
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See how those are the same whenever we subtract fractions; this becomes 3/8.
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If the probability of him not picking the correct marble is 5/8,
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then the probability of him actually picking the correct marble is going to be 3/8
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because together they have to make up 1 whole.
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1 whole is going to be 100 percent; it is going to be all of it.
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He is either going to pick the correct one or he is going to not pick the correct one.
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These two numbers together have to add up to 1 whole.
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That is it for this lesson; thank you for watching Educator.com.