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

Summary

This video script explores the concept of probability, defined as the ratio of favorable outcomes to possible outcomes. It uses examples like a fair coin toss, a die roll, and a deck of cards to illustrate how probabilities are calculated. The script clarifies that probabilities range from 0 (impossible) to 1 (certain), and it covers scenarios like getting a head on a coin toss (50%), rolling a 3 on a die (16.67%), picking a jack (7.69%), or a face card (23.08%) from a standard deck.

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 is 1, as all outcomes (1-6) are natural numbers.
• 🔢 Probability ranges from 0 (impossible event) to 1 (certain event).
• 📐 Probability (P) is defined as the number of ways an event can occur divided by 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 equally likely outcomes.
• 🎯 When rolling a fair die, the probability of getting a specific number like 3 is 1/6, as there's one favorable outcome out of six possible.
• 🃏 The probability of getting an odd number on a die roll is 3/6 or 50%, with three favorable outcomes (1, 3, 5) out of six possible.
• 🃏 In a 52-card deck, the probability of picking a jack is 4/52, reflecting the four jacks among the total cards.
• 🃏 Similarly, the probability of picking a face card (jack, queen, king) from a 52-card deck is 12/52, considering there are 12 face cards in total.
• 📚 These examples illustrate common probability problems, which will be further explored in future sessions.

Q & A

What is the probability of a pig flying?

The probability of a pig flying is zero, as it is an impossible event.

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

The probability is 1, or 100%, since a fair die will always land on a natural number between 1 and 6.

What does a probability of 0 signify?

A probability of 0 signifies a 0% chance of an event occurring, meaning the event is impossible.

What does a probability of 1 signify?

A probability of 1 signifies a 100% chance of an event occurring, meaning the event is certain.

What is the range of probabilities for any event?

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

How is probability defined mathematically?

The probability of an event occurring, denoted as 'P', is the number of ways in which 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 of getting a head when tossing a fair coin is 1/2 or 50%, as there is one way to get a head and two possible outcomes.

What is the probability of rolling a 3 with a fair die?

The probability of rolling a 3 with a fair die is 1/6, as there is one way to get a 3 and six possible outcomes.

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

The probability of getting an odd number when rolling a fair die is 3/6 or 50%, as there are three odd numbers (1, 3, 5) and six possible outcomes.

What is the probability of picking a jack from a pack of 52 cards?

The probability of picking a jack from a pack of 52 cards is 4/52, as there are four jacks and 52 possible cards to pick from.

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

The probability of picking a face card from a pack of 52 cards is 12/52, as there are 12 face cards (jack, queen, king for each suit) and 52 possible cards to pick from.

Outlines

00:00

🎲 Understanding Probability Basics

The paragraph introduces the concept of probability with two examples: 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 probabilities range from 0 to 1, where 0 indicates an impossible event and 1 signifies a certain event. The paragraph then defines probability as the ratio of the number of favorable outcomes to the total number of possible outcomes. Three examples are given to illustrate this: a fair coin toss (probability of 50% for heads or tails), rolling a die to get a specific number like 3 (probability of approximately 16.67%), and getting an odd number (probability of 50%). The paragraph concludes with a teaser for future sessions that will delve into more problems based on these examples.

Keywords

💡Probability

Probability refers to the measure of the likelihood that a particular event will occur. In the video, it is defined as the number of ways an event can occur divided by the total number of possible events. This concept is central to the video's theme, as it is used to explain various scenarios such as the impossibility of a pig flying (probability of 0) and the certainty of rolling a natural number on a die (probability of 1).

💡Natural Number

A natural number is a positive integer, typically used to count objects. In the context of the video, the script explains that when rolling a fair die, one will always get a natural number between 1 and 6, as these are the only outcomes possible. This illustrates the concept of a certain event, where the probability is 1.

💡Fair Die

A fair die is a cube-shaped object with each of its six faces showing a different number from 1 to 6. The video uses the fair die as an example to explain how probability works, with each face having an equal chance of landing face up, thus each number having a probability of 1/6 when the die is rolled.

💡Event

An event is a particular outcome or set of outcomes in a probabilistic situation. The video script discusses events in terms of their likelihood, such as the event of getting a head when tossing a coin or getting an odd number when rolling a die. Understanding events is crucial for calculating probabilities.

💡Coin Toss

A coin toss is a simple random experiment where a coin is flipped, and the outcome is either heads or tails. The video uses the coin toss to illustrate the concept of probability, stating that the probability of getting a head or a tail is 1/2 or 50%, as there are two equally likely outcomes.

💡Odd Number

An odd number is an integer which is not a multiple of two. The video explains the probability of rolling an odd number on a die as an example of how to calculate the probability of an event that has more than one favorable outcome. With three odd numbers (1, 3, and 5) out of six possible outcomes, the probability is 3/6 or 50%.

💡Face Card

In a standard deck of playing cards, face cards refer to the cards with pictures of people: Jacks, Queens, and Kings. The video uses the probability of drawing a face card from a deck of 52 cards to demonstrate how to calculate probabilities when there are multiple favorable outcomes (12 face cards out of 52).

💡Certain Event

A certain event is one that will always occur, having a probability of 1. The video uses the example of rolling a natural number on a fair die to illustrate a certain event, as the outcome will always be a number between 1 and 6.

💡Impossible Event

An impossible event is one that cannot occur, having a probability of 0. The video uses the humorous example of a pig flying to explain an impossible event, as pigs are not capable of flight, making the probability of this event zero.

💡Total Number of Possible Events

This term refers to the sum of all possible outcomes in a given experiment. The video explains that to calculate the probability of an event, one must consider the number of ways the event can occur and divide it by the total number of possible events. This is demonstrated in examples such as the coin toss and die roll.

Highlights

Probability of a pig flying is zero, as pigs cannot fly.

Probability of rolling a natural number on a fair die is 1, as all outcomes (1-6) are natural numbers.

Probability of 0 indicates a 0% chance of an event occurring, making it an impossible event.

Probability of 1 indicates a 100% chance of an event occurring, making it a certain event.

Every event's probability lies between 0 and 1, inclusive.

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

Probability of getting a head on a fair coin toss is 1/2 or 50%.

Probability of getting a tail on a fair coin toss is also 1/2 or 50%.

Probability of rolling a 3 on a fair die is 1/6.

Probability of rolling an odd number on a fair die is 3/6 or 50%.

Probability of picking a jack from a pack of 52 cards is 4/52.

Probability of picking a face card from a pack of 52 cards is 12/52.

The three examples used to explain probability are coin toss, die roll, and card draw.

These examples are common in exam problems related to probability.

Future sessions will solve more problems based on these examples.

Transcripts

What is probability?

Let me start off with a question.

What is the probability of a pig flying?

Can a pig fly?

No, it cannot!

The probability of a pig being able to fly is zero.

Okay, another one.

What is the probability of getting a natural number

on the roll of a fair die?

No matter how the die is rolled,

you will get a number between 1 and 6,

all of which are natural numbers.

The probability is 1.

We will definitely get a natural number

on the roll of a fair die.

A probability of 0 also means

there is a 0% chance of the event occurring.

It's an impossible event!

On the other hand, a probability of 1

tells us there is a hundred percent chance of the event occurring.

It is a certain event.

That brings us to an important point in the video.

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

But how is it actually defined?

What is probability?

Let's call it 'P'.

The probability of an event occurring

is the number of ways in which an event can occur

over the total number of possible events.

Number of ways an event can occur,

over the total number of events.

To understand this well, we look at three examples!

First, the toss of a fair coin.

It can either land a head or a tail.

Now listen to this carefully.

If we toss a fair coin,

what is the probability that it will land a head?

We're just tossing one coin.

What is the probability that we will get a head?

What is the number of ways in which we can get a head?

There's only one way and that's if it lands a head.

And what are the total possible events?

We can get a head or a tail.

Two total events.

So the probability of getting a head at the toss of one fair coin

is '1 over 2'

or 50%.

What is the probability of getting a tail then?

There's only one way in which we can get a tail .

And there are two possibilities.

Probability of getting a tail at the toss of a coin is also 50%.

Now let's look at the case of a fair die.

If we roll a fair die,

it will land one of these six numbers.

What is the probability that the die will land a 3?

This one's easy.

There's only one way in which we can get a three.

And there are a total of six possibilities.

The probability of getting a three at the role of a die

is 'one over six'.

It's slightly on the lower side.

Okay, so what would be the probability of

getting an odd number at the throw off a fair die?

There are three ways in which we can get an odd number

and there are a total of six possibilities.

So the probability of getting an odd number at the throw of a fair die

is 'three over six' of 50%.

And the last example is that of a pack of cards.

Let's assume a pack of 52 cards.

Say we pick a random card from this pack.

What is the probability that we will pick a jack?

Think logically!

How many jacks are there in the entire pack?

There are four jacks.

One in each suit

and the total number of cards is 52.

The probability of picking a jack from a pack of 52 cards,

is '4 over 52' .

And here's the last question in this session.

What is the probability of picking a face card?

There are 12 face cards.

Jack, queen and king in each of the four suits.

And the total number of possibilities is 52.

The probability of picking a face card from a pack of 52 cards,

is '12 over 52'.

These are the three most common types of

problems seen in the exams.

In the coming sessions,

we will solve more problems based on these three examples.