Probabilty is an integral part of class 11 maths syllabus and has importance for not only the class 11 exams but also for different engineering exams like JEE. here, a brief introduction to probability is given based on the class 11 maths syllabus which will help to learn the related concepts quickly.
Probability for Class 9: Key Concepts
- An experiment is said to be a random experiment if there are more than one possible outcomes and it’s impossible to predict the outcome in advance.
- All possible results of an experiment are called its outcome.
- Let us consider an experiment of rolling a die. All possible outcomes are 6, 5, 4, 3, 2, or 1. The set of all these outcomes {6, 5, 4, 3, 2, 1} is known as the sample space (denoted by ‘S’).
- Let us consider an experiment of tossing Two coins once. Since either coin can turn up Tail or Head, therefore, all the possible outcomes are Both coins – Head = HH, Both coins – Tail = TT, First coin – Head and Second coin – Tail = HT, First coin – Tail and second coin – Head = TH. Therefore, the sample space (S) can be represented as = {HT, TT, TH, HH,}.
- For any random experiment, Let S be the sample space. The probability P is a real-valued function whose domain is the power set of S and [0,1] is the range interval.
- For any event E,P(E)≥0
- P(S) = 1
- If E and F are mutually exclusive events, then \(P(E \cup F) = P(E) + P(F)\)
Events in Probability
The set of all possible outcomes is known as the Sample space. All elements of a sample space are known as Sample points. An event is a subset of the S (sample space). An empty set is also known as the Impossible event. The set A′ is known as the Complementary event.
- Event P or Q: The set P ∪ Q
- Event P and Q: The set P ∩ Q
- Event P and not Q: The set P – Q
- P and Q are mutually exclusive if P ∩ Q = φ
- Events P1, P2, . . . . . , Pn are exhaustive and mutually exclusive if P1 ∪ P2 ∪ . . . . . ∪ Pn = S and Ei ∩ Ej = φ V i ≠ j.
If P and Q are two events, then P(P or Q) = P(P) + P(Q) – P(P and Q) and P(P ∪ Q) = P(P) + P(Q) – P(P ∩ Q)
- If P and Q are mutually exclusive, then P(P or Q) = P(P) + P(Q)
- If M is an event, then P(not M) = 1 – P(M)
Probability Class 11 Practice Questions
Also Read
| Bays Theorem | Probability Distribution of Random Variable |
| Total Probability Theorem | Multiplication Rule of Probability |
