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}



Sample Space Word Problems

Problem 1:

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

Solution:

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.
Problem 2:

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

Solution:

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.
Problem 3:

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.

Solution:

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

Hence, number of possible outcomes are 9.