In many real life events there is no certainty of the outcome but there are a certain number of possible outcomes. For example, when we toss a coin we are uncertain about the outcome but we know that there can be only two outcomes, head and tail. This set of possible outcomes is known as sample space.

**Example ****1: **

What is the sample space when two coins are tossed?

**Solution: **

The sample space for one coin tossed is {H, T}.

The possibilities when two coins are tosses are {H, H}, {H, T}, {T, H}, and {T, T}.

Hence, there are four possibilities.

Sample space, S = {(H,H),(H,T),(T,H),(T,T)}

**Example 2****: **

Find the sample space in choosing an integer from the interval [2, 8].

Solution:

As the given interval is closed, the integers in the interval [2, 8] are 2, 3, 4, 5, 6, 7, 8.

The integer chosen can be any of these integers.

Hence, sample space S = {2, 3, 4, 5, 6, 7, 8}

What is the sample space when two coins are tossed?

The sample space for one coin tossed is {H, T}.

The possibilities when two coins are tosses are {H, H}, {H, T}, {T, H}, and {T, T}.

Hence, there are four possibilities.

Sample space, S = {(H,H),(H,T),(T,H),(T,T)}

Find the sample space in choosing an integer from the interval [2, 8].

Solution:

As the given interval is closed, the integers in the interval [2, 8] are 2, 3, 4, 5, 6, 7, 8.

The integer chosen can be any of these integers.

Hence, sample space S = {2, 3, 4, 5, 6, 7, 8}

What is the number of possible outcomes when two dices are rolled?

Sample space when one dice is rolled = {1, 2, 3, 4, 5, 6}

Sample space of two dices, S = {(1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Number of possible outcomes = 36.

Asha has one white, one green shirt and one black and one gray jeans. How many ways are there for her to dress up?

Sample space, S = {green shirt and black jeans, green shirt and gray jeans, white shirt and black jeans, white shirt and gray jeans}

The number of ways she can dress up is 4.

A bag has 2 red balls, 3 green balls and 4 orange balls. Find the number of possible outcomes when one ball is chosen randomly from the bag.

The one ball chosen can be any one of 2 red, 3 green and 4 orange balls.

Hence, number of possible outcomes are 9.