Question

Prove with the help of example: ⭐Event is a subset of a sample space ⭐​

Answer 1

Step-by-step explanation:

The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S. Any subset E of the sample space S is called an event.

some Examples

Sample space is all the possible outcomes of an event. Sometimes the sample space is easy to determine. For example, if you roll a dice, 6 things could happen. You could roll a 1, 2, 3, 4, 5, or 6.

• When dealing with any type of probability question, the sample space represents the set or collection of all possible outcomes. In other words, it is a list of every possible result when running the experiment just once. For example, in one roll of a die, a 1, 2, 3, 4, 5, or 6 could come up.

Answer 2

Answer:

Event is a subset of the sample space.

Step-by-step-explanation:

Event is a set of favourbale outcomes of the given sample space.

Let's take an example of two-coins are tossed.

The sample space of two-coins tossed is given by,

S = { HH, HT, TH, TT } - - ( 1 )

Let A be the event that the coin tossed having all heads.

A = { HH } - - ( 2 )

From ( 1 ) & ( 2 ), we can say that,

A is subset of S.

∴ An event is a subset of a sample space.

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Additional Information:

1. Set :

The group of well defined objects is known as 'set'.

Ex. : A set of days in a week.

2. Types of set:

There are total four types of sets.

A. Singleton set.

B. Empty set or Null set.

C. Finite set.

D. Infinite set.

3. Methods of writing a set:

A. Listing method:

X = { 1, 3, 5, 7, 9 }

B. Roster form or Rule method:

X = { x | x is an odd number, x ∈ N, x ≤ 1 }

4. Union of two sets:

The set formed by the union of all elements in two sets, is called Union of two sets.

5. Intersection of two sets:

The set formed by only common elements in two sets, is called Intersection of two sets.

6. Addition of two sets:

The union of all elements in two sets is called the addition of two sets. It is same as the Union of two sets.

7. Subtraction of two sets:

The set formed by removing common elements from one of the two sets, is called Subtraction of two sets.

8. Subset:

When the elements of a set are involved in other set, then the second set is known as subset of the first.

For example,

A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

B = { 2, 4, 6, 8, 10 }

The all elements of set B are there in the set A.

∴ B is subset of A.

It can be written as - B ⊆ A