Probability Chapter Notes - Mathematics (Maths) Class 10

Basic Terms

• Probability: Probability is a concept which numerically measures degree of certainty of the occurrence of events.
• Experiment: An operation which can produce some well-defined outcomes is called an experiment.
• Random Experiment: An experiment in which all possible outcomes are known.
• Trial: means performing a random experiment
• Outcomes: An outcome is what comes out as a result of a random test or trial.

What is Probability?

Probability is a way to understand how likely something is to happen using numbers. It's like measuring how uncertain an event's outcome is. We use a scale from 0 to 1, where 0 means it can't happen at all, and 1 means it's certain to happen. You can also think of this scale as percentages, where 0% means impossible and 100% means certain.

For example , if we flip a coin, the chance of getting heads is the same as the chance of getting tails, both 1/2 or 50%. When we add these chances, we get a total probability of 1.

Different Types of Events

Event and Outcome:

An outcome is the result of something random, like rolling a dice and getting a certain number. An event is a collection of outcomes, like rolling a dice and hoping for a number less than five.

Experimental Probability:

This is when we do an experiment many times and see how often an event happens. For example, if a shopkeeper sells 15 balls and 6 of them are red, the probability of selling a red ball on the next day is 6/15 or 2/5.

Theoretical Probability:

Here, we assume all outcomes are equally likely. If you pick a ball from a basket with 5 red and 7 blue balls, the probability of getting a red ball is 5/12.

Elementary Event:

This is when there's only one possible outcome, like flipping a coin and getting heads or tails.

Sum of Probabilities:

If you add up the probabilities of all possible outcomes, it should equal 1. Like when you flip a coin, the probability of heads plus the probability of tails equals 1.

Impossible and Sure Events:

An impossible event has a probability of 0, like rolling a 7 on a regular dice. A sure event has a probability of 1, like getting a number less than 7 when you throw a dice.

Range of Probability:

Probabilities range between 0 and 1, where 0 means impossible and 1 means certain.

Geometric Probability:

This is about calculating the chance of hitting a specific area on a shape. It involves dividing the desired area by the total area.

Complementary Events:

These are two outcomes that cover all possibilities, like getting heads or tails when flipping a coin. If one event is the opposite of the other, they're complementary.

Example 1 : Find the probability of getting a head when a coin is tossed once. Also

find the probability of getting a tail.

Solution : In the experiment of tossing a coin once, the number of possible outcomes

is two — Head (H) and Tail (T). Let E be the event ‘getting a head’. The number of

outcomes favourable to E, (i.e., of getting a head) is 1. Therefore,

P(E) = P (head) =

Number of outcomes favourable to E

Number of all possible outcomes

 =1/2

Similarly, if F is the event ‘getting a tail’, then

P(F) = P(tail) =1/2

Probability of Occurrence of an Event

For example, what is the probability of the getting head, when we toss the coin.
Possible Outcomes when we toss a coin: Head or Tail
So, we have two possible outcomes.
So, number of possible outcomes =2
Favorable outcomes/Outcome: Head will occur
So, we have only one favorable outcome
Probability is given as

Examples

Example of Experiment: 

(a) Tossing A Coin

If we toss a coin, it would be head or tail, only two outcomes.

(b) Tossing A Dice

A dice has six outcomes, numbering 1 to 6.

Example of Experiment: Deck of Cards

A deck of playing cards contains 52 Cards.

If we pick any card from the deck, the outcome will be any one card out of these 52.
There are 13 sets of same type of card. The 4 types of cards are Club, diamond, hearts and Spade.
Heart and spade are red in color, while club and diamond are black in color.

So, there are 13 club, 13 spade, total 26 Black Cards; and 13 hearts, 13 spade total of 26 red cards.

There are 3 face cards in each set.
Jack, Queen and king.
So, there are 3 face cards on each of the 4 sets. So, there are 12 face cards.
Also, we can say there are 6 black face cards, and 6 red face cards.
Apart from face cards, other cards are A, and cards numbering 2 to 10.

Example of Experiment: Tossing two dice

Now, there will be 6 outcomes of each dice, multiplied we will get 6×6 = 62 =36 Outcomes. They are: