A∩B Formula

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 Formula

A∩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