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 
What is A Intersection 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}
What Is P(A∩B) Formula?
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(AB)P(B) or P(A∩B) = P(BA)P(A)
Number of Elements in A∩B
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(AB)P(B) or P(A∩B) = P(BA)P(A)
Related Topics on A∩B Formula
Examples Using A∩B Formula

Example 1: Two sets A and B are given as A = {2, 4, 6, 8, 10} and B = {1, 2, 3, 4, 5, 6}. Find A∩B.
Solution: We need to determine A intersection B, that is, elements that are common in both A and B. As we can see, the common elements are 2, 4, 6.
A∩B = {2, 4, 6}
Answer: Therefore, A∩B = {2, 4, 6}

Example 2: What is the probability of selecting a red card and a 6 when a card is randomly selected from a deck of 52 cards? Solve this by using the P(A∩B) formula.
Solution: Let A and B be the individual probabilities of getting a red card and getting a 6 respectively.
We know that the number of red cards = 26,
The number of 6 labeled cards = 4, and
The probability of getting a red card from a deck of 52 cards, P(A) = 26/52
Since the probability of getting a red card and the probability of getting a 6 are calculated individually here, therefore the total number of cards for both cases will be taken as 52.
Thus, probability of getting a 6 from a deck of 52 cards, P(B) = 4/52
Using the P(A∩B) formula,
P(A∩B) = P(A) × P(B)
P(A∩B) = 26/52 × 4/52
= (26×4)/(52×52)
= 2/52
= 1/26
Answer: The required probability = 1 / 26.

Example 3: What is the probability of getting a 2 and 3 when a die is rolled? Solve this by using the P(A∩B) formula.
Solution: To find: The probability of getting a 2 and 3 when a die is rolled.
Let A and B be the events of getting a 2 and getting a 3 when a die is rolled.
Then, P(A) = 1 / 6 and P(B) = 1 / 6.
Using the P(A∩B) formula,
P(A∩B) = P(A) × P(B)
In this case, A and B are mutually exclusive as we cannot get 2 and 3 in the same roll of a die.
Hence, P(A∩B) = 0.
Answer: The required probability = 0.
FAQs on A∩B Formula
What is A∩B Formula in Set Theory?
Using the definition of the intersection of sets, A intersection B formula is: A∩B = {x: x ∈ A and x ∈ B}
What Is P(A∩B) Formula?
P(A∩B) is the probability of both independent events “A” and "B" happening together, P(A∩B) formula can be written as 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”
How Do you Find A ∩ B?
A ∩ B can be determined by considering only the elements that are present in both A and B. A ∩ B consists the common elements only.
What Does (A ∩ B) Represent in P(A ∩ B) Formula?
(A ∩ B) in P(A ∩ B) Formula represents the intersection of two events A and B. Symbol '∩' denotes intersection.
How To Apply P(A ∩ B) Formula?
We apply P(A ∩ B) formula to calculate the probability of two independent events A and B occurring together. It is given as, P(A∩B) = P(A) × P(B), where, P(A) is Probability of an event “A” and P(B) = Probability of an event “B”.
How Do You Find the P(A ∩ B) Formula of Two Independent Events?
We can find the probability of the intersection of two independent events as, P(A∩B) = P(A) × P(B), where, P(A) is the Probability of an event “A” and P(B) = Probability of an event “B” and P(A∩B) is Probability of both independent events “A” and "B" happening together.
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