Will India win the match today? Will it rain today? These are some common statements which can easily be linked with the concept of probability. In mathematical terms, the probability is the analysis of how likely is an event to occur. The chapter on Probability class 10 Maths denotes some simple ways of conducting this analysis. Are you a class 10 student? Here are some awesome study notes on Probability class 10 which can help you ace this topic!

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## Introduction to Probability Class 10

NCERT chapter on Probability class 10 explains the essence of probability with some outstanding examples. It helps you guess the outputs of day-to-day experiments. For example, an online poll asking ‘yes or no’ for a game’s result is a probability. Tossing a coin for the head or tail outcome is also an excellent example.

## Types of Probability

Probability has three concepts that make up the whole probability structure which are as follows:

### Experimental

Probability developed over time, and many experimented with various quantities to analyse the outcomes. For example, experimenting with the coin provides either a head or a tail. Such hands-on experiments make up experimental or empirical probability.

**Experimental probability P(E) = Number of trials in which the event happened / Total number of trials**

This formula helps detect the number of times a probable outcome would show up during an event. Here, E represents the event. Also, the class 9 probability experiment discusses probability with a 1000 times coin toss. The outcomes had a probability of 455 heads: 545 tails.

**Theoretical Probability**

People from centuries across the world tried experiments with the coins and got a probability average of ½. For example, French naturalist Comte de Buffon got 2048 heads out of tossing the coin for 4048 times. That means 2048 heads: 2000 tails. Similarly, J.E. Kerrich and Karl Pearson got the same results.

From the inference, if asked the head’s probability for tossing a coin 1000 times, we would say it 500 times, right? The results based on many experiments help us assume the probability. We call this approach to the theoretical probability. The following formula represents the concept.

**Theoretical probability P(E) = Number of outcomes favourable to E / Number of all possible outcomes of the experiment**

**Equally likely outcomes**

The theoretical probability gives a lead to the possible outcomes. We can also call it equally likely. For instance, the probability of a red ball out of three different colours is 1/3. As you can guess the result, it is an equally likely outcome. In probability class 10, we consider every experiment with the equally likely approach.

## Types of Events in Probability

Some of the important probability events are:

Types of Events |
Explanation |

Impossible and Sure Events | If the probability of occurrence of an event is ZERO, it is called an Impossible Event.If the probability of occurrence of an event is ONE, it is called Sure Evevnt. |

Simple Events | Any event which consists of a single point of sample space is known as Simple Event. |

Independent Events and Dependent Events | If the occurrence of an event is not affected by the occurrence of another event, it is known as an Independent Event.Events which are affected by the occurrence of other events are known as Dependent Events. |

Compound Events | When an event consists of more than one single point of sample space, such an event is known as Compound Event. |

Mutually Exclusive Events | When the occurrence of one event excludes or does not take into consideration the occurrence of another event, such events are Mutually Exclusive. They do not have any common point. |

Complementary Events | For any Event there exists another Event. It represents the remaining elements of the sample space. |

Events Associated with AND | If two different events, E1 and E2 are associated with each other with an AND, it means the intersection of events is common to both the events. |

## What are Events in Probability?

Apart from the above categories, NCERT solutions of class 10 maths also have four other types based on the events. It includes:

### Elementary events

The events with a single outcome fall under elementary events. For example, what is the chance of getting 1 when swirling a dice once? The probability is one. What’s the probability of getting 2? Again, the probability would be one. This remains the same for all the other numerals in a die. So, by using the theoretical probability approach,

Theoretical probability P(E) = Number of outcomes favourable to E / Number of all possible outcomes of the experiment

Probability of getting 3 = 1/6

Summing up all the chances, we get 6/6 = 1. Thus, the outcome of any elementary event turns out to be 1.

Similarly, what’s the chance rate of eight in dice if the condition is (4,4)? There is only one chance.

**Complementary Events**

Here, the sum of probabilities may turn out as 1, but the events have different probabilities.

For example, Ram throws the dice on the floor. How many times will eight pop-up, and how many times will four show up? Let P(8) be times the eight on the light and P(4) be the chances for four. By using the theoretical or equally likely method, the possibilities are,

P(8) = 5/12 = 1/4

Similarly,

P(4) = 3/12

Summing up the events, we get:

P(8) + P(4) = 5/12 + 3/12 = 1

As you can see, the average of the chances comes out as 1. However, the event outcomes are different. P(8) is not equal to P(4). Therefore, P (4) =1 – P(8)

**Impossible Events**

The name itself implies the outcome. Yes, the possibilities of the outcomes are zero, thus indicating an impossible event. Look at the example below.

A bag contains balls of three different colours, yellow, green, and orange. What is the probability of a violet ball? Is it workable, or can you assume it? It’s clear that the chances are zero. Thus, P(V) = 0/3 = 0

### Sure Events

Analysing the previous example in a unique perspective helps you comprehend the “sure events”. Taking the bag with three different colours, the outcomes in terms of equally likely are three. Thus, the number of expected outcomes equals the content in the bag. Representing it in the numerical form projects – 3/3 = 1

**Also Read: Class 10 Quadratic Equations**

## What is **Inference** in Probability Class 10?

Inference, in general, is defined as the process of analyzing different results to conclude the data on random variation. The common observation around probability class 10 states that its value can never be less than 0 or greater than 1. From the examples, it’s evident that the favourable results from an event are less than or equal to the total number of outcomes. The following condition iterates the above statement:

*0≤ P(E) ≤1 **i.e., the aspired outcome of an event is always less than or equal to the number of outcomes.*

## Important Tips

### Cards: A pack of playing cards has:

- Four Hearts
- Four Spades
- Four Diamonds
- Four Clubs

### Coin: A Coin has two faces known as:

- Head
- Tail

### Dice: A dice is used in games. It is a small cube, it has:

- Six numbers or spots on its sides
- There will be six outcomes of each dice. It will be multiplied: 6×6 = 36 outcomes

1 | 2 | 3 | 4 | 5 | 6 | |

1 | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) |

2 | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) |

3 | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) |

4 | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) |

5 | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) |

6 | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) |

## Probability Class 10 Solved Examples

**Example 1- A bag contains three red balls and five black balls. A ball is drawn on a guess. What’s the probability of the ball drawn to be (i) red? (ii) not red?**

The number of possible chances is 3+5 = 8

Let P(R) represent the red balls and P(B) the black outcomes.

So,

P(R) = 3/8

And P(B) = 5/8

Sum of the probabilities will turn out as 3/8 + 5/8

*The probability pop-up was 1*

*Example 2 – A box contains five red marbles, eight white marbles and four green marbles. A marble is taken out of the box randomly. What would be the probability of drawn marble to be(i) red?(ii) white?(iii) not green?*

Total chances are 5+8+4 = 17

P(R), P(W) and P(N) represent the outcome of the red, white and not green events, respectively.

So, P(R) = 5/17, P(W) = 8/17

Total probable outcomes come out as 5/17 + 8/17 + 4/17

P(N) = 1- PN = 17/17 – 4/17

Where 4/17 = favourable outcomes for the event P(G)

*The probability is 13/17*

**Practice** Question

A bag contains lemon flavoured candies only. Harish takes out one candy without looking into the bag. What’s the probability that he takes out:

(i) an orange-flavoured candy?

(ii) a lemon-flavoured candy?

Try to find the answer to the above problem. Please share your outcomes in the comment section below.

So, we believe this piece would have helped you to hone in your class 10 probability knowledge NCERT solutions of class 10 maths. Other than this, our domain has various programs handpicked for you to benefit. Keep checking Leverage Edu for more study notes and exam preparation tips!