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Probability is the branch of mathematics that deals with randomness and uncertainty. In general terms, probability is defined as possibilities. It is expressed as a number between 0 and 1. It has been introduced to determine how different outcomes arrive in uncertain situations. It is used in various fields such as science, finance, artificial intelligence, statistics, decision making, etc. Generally, probability means the extent to which something is likely to happen. The concept of probability occurs from the games of chance, but now it's evolved into a rigorous mathematical discipline. It helps us to answer questions like, what is the chance of getting tails during flipping a coin? Or what is the probability of getting 6 while rolling a dice? Etc. Now, to answer these, we should know the total number of possible outcomes. The basic theory of probability is also used in the probability distribution, where we will learn to determine the possible outcomes for the random experiments.
CBSE Class 14 chapter Probability also includes a definition of probability? 'How do we calculate the probability of a single event or multiple events?', 'What are the different types of probability? These topics can be easily downloaded from the Class 10 Maths chapter 14 notes PDF. Along with this, NCERT class 10th maths notes serve as your principal resource for exam preparation, and the NCERT Notes facilitate linking present educational content to both prior lessons and upcoming material.
Probability is defined as a measure of the possibility or chance that a particular event will occur. It assesses uncertainty and is used to determine the outcomes in various situations, from everyday life to scientific research.
Probability is expressed as a number between 0 and 1, which implies 0 means an event is impossible (e.g., rolling an 8 on a standard dice) and 1 means an event is certain (e.g., the sun rising tomorrow). In other terms, it is also represented as a percentage, where 100% means a specific event and 0% means an impossible event. A probability between 0 and 1 represents the degree of possibility of an event occurring. Probability of an Event E is represented by P(E).
Experimental Probability is founded on real-world observations and experimentation. It applies to any occurrence related to an experiment that is carried out numerous times.
The Experimental probability is calculated as follows:
P(E) =
Theoretical Probability is calculated by mathematical methods instead of experimental research or without conducting experiments.
For an event
People use probability for multiple purposes, including statistics and gaming as well as finance and artificial intelligence for deciding and predicting future risks.
0 ≤ P(E) ≤ 1 for any Event E
P(heads) = 0.5
P(tails) = 0.5
They are both elementary events.
So, P(heads) + P(tails) = 0.5 + 0.5 = 1
A process generates various possible end results (e.g., rolling a die).
The set of all possible outcomes of an experiment (e.g., {1, 2, 3, 4, 5, 6} for a die roll) is called as Sample Space.
For example,
A coin is tossed, and it is called an Event.
E1 = Having a head (H) on the upper face when tossed.
E2 = Having a tail (T) on the upper face when tossed.
So, in this case, the possible outcomes are Heads or Tails
Therefore, S = {H, T}
A subset of possible experimental outcomes which shows particular outcomes or collections of outcomes (e.g., rolling an even number).
A measure of the likelihood of an event occurring, calculated as:
The probability of an event not occurring is called the complementary event.
The event
For example, Flipping of a Coin, where ‘getting a tail’ complemented the event of ‘getting a head’.
An event having only one outcome of the experiment is called an Elementary Event.
For example, when rolling a six-sided die, the sample space is:
S = {1, 2, 3, 4, 5, 6}
In this case, each outcome (1, 2, 3, 4, 5, or 6) is an elementary event because it consists of a single outcome.
Like,
Getting a 1 → E = {1}
Getting a 4 → E = {4}
Each of these events has a probability of: P(E) =
An impossible event describes any outcome which will never occur within a particular experiment. It holds true that every impossible event will have a probability value of zero.
For example, the probability of getting a number 8 in a single throw of a die is 0. As 8 can never be the outcome.
A sure event stands as an event which necessarily occurs throughout a particular experiment. A sure event (certain event) holds a fixed probability value of one.
For example, the probability of getting a number less than 7 in a single throw of a die is 1 because it is certain that when a die is thrown once, we will always receive a number less than seven. After all, each face of the die is marked with a number less than seven. Thus, there are six alternative outcomes, which is the same number of favorable options.
The comprehension of probability remains essential for satisfying decision-making processes when uncertainty exists in domains of finance, games, science and technology. Statistical inference, along with machine learning, stands upon probability as its basis, therefore making probability an essential mathematical concept linked to various domains.
Students must download the notes below for each chapter to ace the topics.
Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.
Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.
To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.
Probability is defined as a measure of the possibility or chance that a particular event will occur. It assesses uncertainty and is used to determine the outcomes in various situations, from everyday life to scientific research. Probability is expressed as a number between 0 and 1.
The fundamental formula for probability is:
Other important formulas include:
Probability of an event not occurring:
Sum of all probabilities of an experiment: P(E1) + P(E2) + ... + P(En) = 1
No, probability always lies between 0 and 1 and can also be equal to 0 or 1.
The set of all possible outcomes of an experiment (e.g., {1, 2, 3, 4, 5, 6} for a die roll) is called as Sample Space.
In this case, sample space: {HH, HT, TH, TT}
Favorable cases (at least one H): {HH, HT, TH}
Probability =
=
In this case, sample space: {HH, HT, TH, TT}
Favorable cases (at least one H): {HH, HT, TH}
Probability =
=
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