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# Probability CBSE NCERT Notes Class 10 Maths Chapter 15 PDF

## Basic Terms Used in Probability

### Experiments

An operation which results in some well defined outcomes is called an experiment.

### Sample Space

The set of all possible outcomes of a random experiment is called sample space.

### Events

A subset of the sample space of a random experiment is called an event.

### Simple Events/Elementary Events

An event having only one outcome of the experiment is called an elementary event.

The sum of the probabilities of all the elementary events of an experiment is 1.

### Compound Events

An event having more than one outcome of the experiment is called compound event.

### Impossible Events

The probability of an event which is impossible to occur is 0. Such an event is called an impossible event. If P(E) = 0 ⇒ E is an impossible event.

### Sure Events

The probability of an event which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event. If P(E) = 1 ⇒ E is a sure event.

### Complementary Events

An event which occurs only when event E does not occur is called complementary event of E and it is denoted by E*‘*.

## Probability Definition

Probability theory is that branch of mathematics in which we numerically study the chances of occurrence of events and it is defined as

## Probability Results

1. 0 ≤ P(E) ≤ 1

2. P(E) ≥ 0 and P(E) ≤ 1

3. P(E) + P(E*‘*) = 1 ⇒ P(E*‘*) = 1 – P(E)

### Class 10 Maths Chapter 15 Examples 1:

Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.

S = {H, T} ⇒ n(S) = 2 and E = {T} ⇒ n(E) = 1.

Thus, required probability is P(E) = n(E)/n(S) = 1/2

### Class 10 Maths Chapter 15 Examples 2:

One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will be an ace.

Number of outcomes Favorable to E = 4 and

Number of Possible Outcomes = 52

Thus, P(E) = 4/52 = 1/13

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