What is Probability? (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise

Infinity Learn NEET
6 Jul 201505:03
EducationalLearning
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TLDRThis video script explores the concept of probability, using relatable examples to illustrate how it's calculated as the ratio of favorable outcomes to total possible outcomes. It clarifies that probabilities range from 0 (impossible events) to 1 (certain events), and provides examples including coin tosses, die rolls, and card draws to demonstrate the calculation of probabilities in various scenarios. The script is designed to demystify the concept and prepare viewers for more complex problems in future sessions.

Takeaways
  • 🐷 The probability of an impossible event, like a pig flying, is zero.
  • 🎲 When rolling a fair die, the probability of getting a natural number between 1 and 6 is 1, as it is a certain event.
  • 🔢 Probability ranges from 0 to 1, where 0 means no chance of occurrence and 1 means certainty.
  • 📐 Probability is defined as the ratio of the number of ways an event can occur to the total number of possible events.
  • 🪙 The probability of getting a head on a fair coin toss is 1/2 or 50%, as there are two possible outcomes.
  • 🎲 The probability of rolling a specific number, like a 3, on a die is 1/6, as there is one favorable outcome out of six.
  • 🃏 The probability of drawing a jack from a standard deck of 52 cards is 4/52, reflecting the number of jacks in the deck.
  • 👤 The probability of drawing a face card from a deck is 12/52, considering there are 12 face cards in total.
  • 🤔 Understanding probability involves considering the number of favorable outcomes over the total possible outcomes.
  • 📚 The script provides three common examples to illustrate probability concepts: coin tosses, dice rolls, and card draws.
  • 📈 The script suggests that further sessions will involve solving more problems based on these examples to deepen understanding.
Q & A

  • What is the probability of a pig flying according to the script?

    -The script states that the probability of a pig flying is zero, indicating an impossible event.

  • What is the probability of rolling a natural number on a fair die?

    -The probability is 1, as a fair die will always land on a natural number between 1 and 6.

  • What does a probability of 0% signify in terms of an event occurring?

    -A probability of 0% means there is no chance of the event occurring, making it an impossible event.

  • What does a probability of 100% signify?

    -A probability of 100% indicates a certain event, meaning the event will definitely occur.

  • What is the range of probability values for any event?

    -The probability of every event will lie between 0 and 1, inclusive.

  • How is the probability of an event defined in the script?

    -The probability of an event, denoted as 'P', is defined as the number of ways an event can occur divided by the total number of possible events.

  • What is the probability of getting a head when tossing a fair coin?

    -The probability is 1/2 or 50%, as there is one way to get a head and two possible outcomes (head or tail).

  • What is the probability of rolling a 3 on a fair die?

    -The probability is 1/6, as there is only one way to roll a 3 and six possible outcomes.

  • What is the probability of getting an odd number when rolling a fair die?

    -The probability is 3/6 or 50%, since there are three odd numbers (1, 3, 5) out of six possible outcomes.

  • What is the probability of picking a jack from a standard deck of 52 cards?

    -The probability is 4/52, as there are four jacks in the deck.

  • What is the probability of picking a face card from a pack of 52 cards?

    -The probability is 12/52, because there are 12 face cards (3 face cards per suit, with 4 suits) in the deck.

Outlines
00:00
🚫 Understanding Probability Basics

This paragraph introduces the concept of probability with two examples to illustrate the extremes: the impossibility of a pig flying (probability of 0) and the certainty of rolling a natural number on a fair die (probability of 1). It emphasizes that all probabilities range between 0 and 1, inclusive. The paragraph then defines probability as the ratio of favorable outcomes to the total possible outcomes and uses the toss of a fair coin to explain this concept further, showing that the probability of getting a head or a tail is 50% each.

🎲 Probabilities in Dice Rolls and Card Draws

The paragraph delves into the probabilities associated with rolling a fair die and drawing cards from a standard deck. It explains that the probability of rolling a specific number, like a 3, is 1 in 6. It also discusses the probability of getting an odd number, which is 50% since there are three odd numbers out of six possible outcomes. The paragraph then shifts to card probabilities, illustrating that the chance of drawing a jack from a 52-card deck is 4 in 52, and the chance of drawing a face card is 12 in 52, highlighting the calculation of probabilities in different scenarios.

Mindmap
Keywords
💡Probability
Probability is a fundamental concept in statistics that quantifies the likelihood of a given event occurring. It is defined as the number of ways an event can occur divided by the total number of possible events. In the video, probability is central to understanding the chances of various outcomes, such as the impossibility of a pig flying (probability of 0) or the certainty of rolling a natural number on a die (probability of 1).
💡Natural Number
A natural number is a positive integer, typically starting from 1. In the context of the video, when rolling a fair die, the outcome will always be a natural number between 1 and 6, inclusive. The script uses this to illustrate a scenario where the probability of the event (rolling a natural number) is 1, indicating a certain event.
💡Fair Die
A fair die refers to a cube-shaped object with six faces, each marked with a different number from 1 to 6, and used in various games and for randomization. The video uses the fair die to explain how the probability of rolling a specific number, like 3, is one out of six, or approximately 16.67%.
💡Event
In probability theory, an event is a set of outcomes of an experiment that can be uniquely identified. The video script discusses different types of events, such as the impossible event of a pig flying and the certain event of rolling a natural number with a fair die, to illustrate the range of probabilities from 0 to 1.
💡Coin Toss
A coin toss is a simple random experiment with two possible outcomes: heads or tails. The video uses the coin toss to demonstrate a 50% probability for each outcome, as there is one way to get heads and one way to get tails out of two possible events.
💡Heads
Heads is one of the two sides of a coin, typically featuring a portrait or emblem. In the video, the probability of a coin landing on heads is given as 50%, which is calculated by having one favorable outcome (landing on heads) over two possible outcomes (heads or tails).
💡Tails
Tails is the opposite side of heads on a coin and represents the other possible outcome of a coin toss. The script explains that the probability of getting tails is also 50%, mirroring the explanation for heads, emphasizing the equal likelihood of both outcomes.
💡Odd Number
An odd number is an integer that is not divisible by two, resulting in a remainder of one. The video uses the roll of a fair die to explain that the probability of rolling an odd number is 50%, as there are three odd numbers (1, 3, 5) out of six possible outcomes.
💡Card Deck
A card deck typically refers to a set of 52 playing cards used in various card games. The video uses a standard deck of cards to illustrate the probability of drawing specific cards, such as a jack or a face card, from the total number of cards available.
💡Jack
A jack is a face card in a deck of playing cards, ranking between the queen and the ten. The script explains that there are four jacks in a standard deck of 52 cards, making the probability of randomly drawing a jack '4 over 52', which simplifies to approximately 7.69%.
💡Face Card
A face card is a playing card with a picture representing the rank of the card, such as a jack, queen, or king. The video uses the concept of face cards to demonstrate that there are 12 face cards in a deck, and thus the probability of drawing a face card is '12 over 52', or about 23.08%.
Highlights

Probability of a pig flying is zero, indicating an impossible event.

Probability of getting a natural number on a fair die roll is 1, a certain event.

All probabilities lie between 0 and 1, inclusive.

Probability is defined as the number of ways an event can occur over the total number of possible events.

Tossing a fair coin has a 50% probability of landing heads or tails.

Rolling a fair die has a 1/6 probability of landing on any specific number.

The probability of getting an odd number on a die roll is 50%.

Picking a jack from a 52-card deck has a probability of 4/52.

There are 12 face cards in a standard 52-card deck.

Picking a face card from a 52-card deck has a probability of 12/52.

Three examples are used to illustrate probability concepts: coin toss, die roll, and card draw.

A probability of 0% means an event will not occur.

A probability of 100% means an event will definitely occur.

Understanding probability involves comparing the number of favorable outcomes to the total outcomes.

The concept of 'ways an event can occur' is crucial for calculating probability.

Examples provided help to understand the practical application of probability in everyday scenarios.

Upcoming sessions will solve more problems based on the three examples of coin, die, and card.

Transcripts

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ProbabilityStatisticsCoin TossDice RollCard DeckMath ConceptsEvent OutcomesFair CoinFair DieCard OddsEducational