What is a Probability
Probability means possibility. It’s a branch of Maths that deals with occurrence of a random event. The value is expressed from zero to one. Probability is introduced in Maths to predict how likely events happen.
The meaning of probability is the extent to which something is likely to happen. This is basic probability theory, which is also used in the probability distribution. You will learn the possibility of outcomes for a random experiment. To find the probability of any single event to happen, we should first know the total number of possible effects.
Basics of CBSE class 12 Applied Maths Probability
Probability is the measure of likelihood of an event to occur. Many circumstances can’t be predicted with total certainty. We can predict only the chance of the event to occur, i.e., how likely they are to happen, using it.
Probability can range from 0 to 1, where 0 means the events to be an impossible one, and 1 indicates a particular event. Probability for Class 12 Applied maths is an essential topic for the students, which explains all the basic concepts of this topic. The probability of all possibilities in a sample space adds up to 1.
Example, when we toss the coin, either we get Head or the Tail, only two possible outcomes are possible.
(H, T). But suppose we toss two coins in the air. In that case, there could be three possibilities of events to occur, such as both the coin show heads or both shows tails or one shows heads and one tail, i.e. (H, H), (H, T), (T, T) there could be three possibilities of events to occur, such as both shows tails or one shows heads and one tail, i.e. (H, H), (H, T), (T, T).
The formula for Applied Maths Probability
The probability formula is known as the possibility of the event to happen is equal to the ratio of number of favorable results and the total number of promising results and the total number of results.
Probability of an event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Sometimes students get mistaken for “favorable outcome” with “desirable outcome.” This is the basic formula. But there are some other formulas for different situations or events.
Types of Probability
- Theoretical Probability
- Experimental Probability
- Axiomatic Probability
Theoretical Probability
It’s based on the possible chances of something to occur. The theoretical probability is based on the reasoning behind probability. Example, if the coin is tossed, the theoretical probability of getting ahead will be 1\2.
Experimental Probability
It is based on the observations of an experiment. The experimental probability could be calculated based on the number of possible outcomes by the total number of trials. Example, if the coin is tossed ten times and heads are recorded six times, the heads’ experimental probability is 6/10 or 3/5.
Axiomatic Probability
In axiomatic probability, a set of axioms are set, which applies to all types. These axioms are set by Kolmogorov and known as Kolmogorov’s three axioms. With the axiomatic approach to probability, chances of occurrence or non-occurrence of the events can be quantified.
Syllabus of the CBSE Class 12 Applied Maths Probability
- Independent and Dependent Events
- Law of Total Probability
- Bayer’s Theorem
The syllabus of class 12 applied maths probability is not very broad as compared to the other topics. It is comparatively an easy topic.
Also check CBSE Class 12 Linear Programming
