A intersection B is a set that contains elements that are common in both sets A and B. The symbol used to denote the intersection of sets A and B is ∩, it is written as A∩B and read as 'A intersection B'. The intersection of two or more sets is the set of elements that are common to every set. A∩B can be determined easily by checking the elements that are present in both A and B. Let us go through the concept of A∩B with the help of some solved examples for a better understanding.
1. What is A Intersection B Formula? 2. What Is P(A∩B) Formula? 3. Number of Elements in A∩B 4. FAQs on A∩B FormulaA∩B is a set that consists of elements that are common in both A and B. The formula A intersection B represents the elements that are present both in A and B and is denoted by A∩B. So, using the definition of the intersection of sets, A intersection B formula is:
A∩B = {x : x ∈ A and x ∈ B}
P(A∩B) is the probability of both independent events “A” and "B" happening together. The symbol "∩" means intersection. This formula is used to quickly predict the result. When events are independent, we can use the multiplication rule, which states that the two events A and B are independent if the occurrence of one event does not change the probability of the other event. P(A∩B) formula can be written as P(A∩B) = P(A) × P(B). P(A∩B) formula is given as:
P(A∩B) Formula
P(A∩B) = P(A) × P(B)
where,
- P(A∩B) = Probability of both independent events “A” and "B" happening together.
- P(A) = Probability of an event “A”
- P(B) = Probability of an event “B”
To calculate P(A∩B) for dependent events, we use the concept of conditional probability and rewrite the formula as,
P(A∩B) = P(A|B)P(B) or P(A∩B) = P(B|A)P(A)
To determine the number of elements in A intersection B, we will use the formula for A union B. We know that the number of elements in A U B is given by n(A U B) = n(A) + n(B) - n(A ∩ B), where
- n(A U B) = Number of elements in A U B
- n(A) = Number of elements in A
- n(B) = Number of elements in B
- n(A ∩ B) = Number of elements in A ∩ B
By taking n(A ∩ B) to one side and all other terms on another side, the formula for the number of elements in A∩B is given as,
n(A∩B) = n(A) + n(B) - n(A U B)
Important Notes on A Intersection B Formula
- A∩B = {x : x ∈ A and x ∈ B}
- A∩B = B∩A
- n(A∩B) = n(A) + n(B) - n(A U B)
- For independent events A and B, P(A∩B) = P(A) × P(B)
- For dependent events A and B, P(A∩B) = P(A|B)P(B) or P(A∩B) = P(B|A)P(A)
Related Topics on A∩B Formula
- Intersection of Events
- A union B formula
- Set Operations