Question

What does intersection mean in probability?

Answer 1

Hint: The term intersection in set theory as well as in probability is almost the same. The intersection in Set theory means that it only contains only the elements which are common in both given sets. Intersections do not only extend up to two sets but also more than two. The notation for the intersection is $A\cap B$ .

Complete step by step solution:
The intersection is a set of elements that are common to both sets, $A,B\;$
The intersection is denoted by the symbol, $A\cap B$
When put into condition format, $x\in A\cap B$ If $x\in A$ and $x\in B$
For example,
Let there be two sets.
A= {red, orange, purple, green, violet}
B= {green, yellow, blue, red, brown}
When we take the intersection of these two sets, $A\cap B$ , We write down the common elements from both sets.
The common elements from both the sets are,
$A\cap B$ = {green, red}
Now that we understood the meaning of intersection in sets,
Let us move on to the intersection in probability.
It is defined by, when there are two events $A,B\;$ , Then the intersection of these two events, $A\cap B$ , is a collection of all the outcomes that are elements in both the sets $A,B\;$
It is mostly described in probability questions as “and”.
To understand better we shall take up an example.
Let us consider two events while rolling dice where,
E: “The number rolled is even” and T: “The number rolled is greater than two”
Then the intersection $E\cap T$ of these two events would be,
Let us first find the sample space.
The sample space is $S=\left\{ 1,2,3,4,5,6 \right\}$
The outcome for E is $E=\left\{ 2,4,6 \right\}$
The outcome for T is $T=\left\{ 4,6 \right\}$
Then the intersection $E\cap T$ of these two events would be a set of common elements,
Hence, $E\cap T=\left\{ 4,6 \right\}$

Note: In the same way as the intersection, there is also a term called Union which is a set of all elements present in both the sets written without any repetition. It is denoted by the symbol, $A\cup B$ .It is mostly described in probability questions as “or”.