This chapter introduces the foundational concepts of probability, emphasizing the significance of events and sample spaces in understanding chance.
Probability – Formula & Equation Sheet
Essential formulas and equations from Mathematics, tailored for Class 11 in Mathematics.
This one-pager compiles key formulas and equations from the Probability chapter of Mathematics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
P(E) = n(E) / n(S)
P(E) is the probability of event E, n(E) is the number of favorable outcomes, and n(S) is the total number of outcomes in the sample space. This formula calculates the probability when all outcomes are equally likely.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
This formula gives the probability of either event A or event B occurring. P(A ∩ B) accounts for the overlap, ensuring outcomes common to both are not double-counted.
P(not A) = 1 - P(A)
This is the probability of the complement of event A occurring. It is useful when the probability of event A is known.
E(A | B) = P(A ∩ B) / P(B)
E(A | B) is the conditional probability of A given B. It calculates the likelihood of event A occurring under the condition that event B has already occurred.
P(A and B) = P(A) * P(B | A)
This formula finds the joint probability of two events A and B occurring. It suggests that the probability of both occurs by multiplying the probability of A by the conditional probability of B given A.
n(S) = n! / (n1! * n2! * ... * nk!)
This is used to calculate the number of permutations of n items with groups of indistinguishable items. n is the total number of items, and n1, n2, ...nk are counts of indistinguishable items.
P(E) = Number of favorable outcomes / Total outcomes
This formula determines the probability of event E occurring in a simple sample space.
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
This formula calculates the probability of both events A and B occurring simultaneously by rearranging the union and intersection probabilities.
P(A1 ∪ A2 ∪ ... ∪ An) = Σ P(Ai) - Σ P(Ai ∩ Aj)
This formula generalizes the probability of the union of multiple events by adding their individual probabilities and subtracting the probabilities of their pairwise intersections.
n(E) = n! / r!(n - r)! (Combination formula)
This calculates the number of ways to choose r elements from a set of n elements, where the order does not matter. Useful in probability distribution calculations.
Equations
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Probability of either A or B happening.
P(A ∩ B) = P(A) * P(B | A)
Joint probability of A and B occurring together.
0 ≤ P(E) ≤ 1
Probability of any event E is between 0 and 1.
P(S) = 1
The probability of the sample space S always equals 1.
P(E) + P(E') = 1
The probability of event E and its complement always sums to 1.
P(E | F) = P(E ∩ F) / P(F)
Conditional probability of E given F.
Σ P(Ei) = 1 for an exhaustive set
The probabilities of all mutually exclusive outcomes sum up to 1.
P(A_i ∩ A_j) = 0 for i ≠ j (if A_i and A_j are mutually exclusive)
The intersection of mutually exclusive events is zero.
E(A) + E(B) = E(A ∪ B) + E(A ∩ B)
Overall event expectation incorporates unions and intersections.
n(E) = n! / (k! * (n-k)!)
Combination formula for calculating outcomes.
This chapter explores the properties and equations of straight lines in coordinate geometry, emphasizing their significance in mathematics and real-life applications.
Start chapterThis chapter explores conic sections including circles, ellipses, parabolas, and hyperbolas, highlighting their definitions and significance in mathematics and real-world applications.
Start chapterThis chapter introduces the essential concepts of three dimensional geometry, focusing on how to represent points in space using coordinate systems.
Start chapterThis chapter introduces fundamental concepts of calculus, focusing on limits and derivatives, which are essential for understanding changes in functions.
Start chapterThis chapter introduces the fundamental concepts of statistics, focusing on data analysis and its importance in making informed decisions.
Start chapter
