Revision Notes on Chance and Probability
Chance and Probability
Probability tells the degree of uncertainty. It measures the likelihood that an event will occur.
Experiment
An operation which can produce some well-defined outcomes is called an experiment.
Each outcome is called event.
Random Experiment
If the result of the experiment is not known then it is called a random experiment.
Example
If we throw a dice then the result could be any number from 1 – 6.
Outcomes
When we do an experiment then there could be different results, these possible results of the random experiment are called outcomes.
Some Experiments and Their Outcomes
Example
Tossing a coin
We get Head OR Tail, only two possible outcomes are possible (H, T).
Tossing Two coins
When two coins are tossed then there will be four possible outcomes are {(H, H), (H, T), (T, H), (T, T)}.
Equally Likely Outcomes
If every outcome has the same possibility of occurring these outcomes are called Equally Likely Outcomes.
Example
If we throw a dice then there is an equal chance of every no. to come while doing the random experiment. i.e. a dice has the same possibility of getting 1, 2, 3, 4, 5 and 6.
Linking Chances to the Probability
Example
What is the chance of getting 3 when we throw a dice?
Solution
There is only one chance to get 3 in one throw and the total possible outcomes are 6.
Hence the probability of getting =1/6.
Outcomes as Events
Each outcome or collection of outcomes of an experiment is called event.
Example
If we throw a dice then getting each outcome 1, 2, 3, 4, 5 and 6 are events.
Example
What is the event of getting odd numbers when we throw a dice?
Solution
The probability of getting an odd number is 3(odd numbers are 1, 3, 5)
The total number of outcomes is 6.
The probability of getting an odd number = 3/6.
Example
What is the probability of spinning yellow?
Here number of chance to come yellow while spinning is 3.
The total number of outcomes is 8.
Drawing a card from a well shuffled deck of 52 cards
Total cards in a deck = 52
We can classify types of cards in a deck in two ways:
Based on Colour of Cards
The suits which are represented by red cards are hearts and diamonds.
While the suits represented by black cards are spades and clubs.
There are 26 red cards and 26 black cards.
Let’s learn about the suits in a deck of cards.
Based on Suits
Suits in a deck of cards are the representations of red and black colour on the cards.
Based on suits, the types of cards in a deck are:
(1) Spades (2) Clubs (3) Hearts (4) Diamonds
There are 52 cards in a deck.
Each card can be categorized into 4 suits constituting 13 cards each.
There is one more categorization of a deck of cards:
Face Cards
These cards are also known as court cards.
They are Kings, Queens, and Jacks in all 4 suits.
Number Cards
All the cards from 2 to 10 in any suit are called the number cards.
These cards have numbers on them along with each suit being equal to the number-on-number cards.
Aces
There are 4 Aces in every deck, 1 of every suit.
Tips and Tricks
Example 1: What is the probability of drawing a king from a deck of cards?
Solution: Here the event E is drawing a king from a deck of cards.
There are 52 cards in a deck of cards.
Hence, total number of outcomes = 52
The number of favourable outcomes = 4 (as there are 4 kings in a deck)
Hence, the probability of this event occurring is
P(E) = 4/52 = 1/13