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.