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What is Probability? (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise - YouTube
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What is probability?
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Let me start off with a question.
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What is the probability of a pig flying?
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Can a pig fly?
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No, it cannot!
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The probability of a pig being able to fly is zero.
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Okay, another one.
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What is the probability of getting a natural number
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on the roll of a fair die?
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No matter how the die is rolled,
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you will get a number between 1 and 6,
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all of which are natural numbers.
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The probability is 1.
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We will definitely get a natural number
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on the roll of a fair die.
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A probability of 0 also means
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there is a 0% chance of the event occurring.
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It's an impossible event!
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On the other hand, a probability of 1
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tells us there is a hundred percent chance of the event occurring.
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It is a certain event.
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That brings us to an important point in the video.
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The probability of every event will lie between '0 and 1' inclusive.
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But how is it actually defined?
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What is probability?
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Let's call it 'P'.
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The probability of an event occurring
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is the number of ways in which an event can occur
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over the total number of possible events.
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Number of ways an event can occur,
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over the total number of events.
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To understand this well, we look at three examples!
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First, the toss of a fair coin.
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It can either land a head or a tail.
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Now listen to this carefully.
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If we toss a fair coin,
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what is the probability that it will land a head?
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We're just tossing one coin.
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What is the probability that we will get a head?
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What is the number of ways in which we can get a head?
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There's only one way and that's if it lands a head.
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And what are the total possible events?
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We can get a head or a tail.
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Two total events.
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So the probability of getting a head at the toss of one fair coin
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is '1 over 2'
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or 50%.
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What is the probability of getting a tail then?
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There's only one way in which we can get a tail .
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And there are two possibilities.
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Probability of getting a tail at the toss of a coin is also 50%.
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Now let's look at the case of a fair die.
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If we roll a fair die,
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it will land one of these six numbers.
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What is the probability that the die will land a 3?
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This one's easy.
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There's only one way in which we can get a three.
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And there are a total of six possibilities.
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The probability of getting a three at the role of a die
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is 'one over six'.
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It's slightly on the lower side.
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Okay, so what would be the probability of
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getting an odd number at the throw off a fair die?
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There are three ways in which we can get an odd number
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and there are a total of six possibilities.
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So the probability of getting an odd number at the throw of a fair die
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is 'three over six' of 50%.
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And the last example is that of a pack of cards.
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Let's assume a pack of 52 cards.
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Say we pick a random card from this pack.
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What is the probability that we will pick a jack?
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Think logically!
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How many jacks are there in the entire pack?
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There are four jacks.
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One in each suit
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and the total number of cards is 52.
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The probability of picking a jack from a pack of 52 cards,
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is '4 over 52' .
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And here's the last question in this session.
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What is the probability of picking a face card?
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There are 12 face cards.
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Jack, queen and king in each of the four suits.
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And the total number of possibilities is 52.
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The probability of picking a face card from a pack of 52 cards,
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is '12 over 52'.
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These are the three most common types of
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problems seen in the exams.
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In the coming sessions,
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we will solve more problems based on these three examples.
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