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Introduction to sample space probability
Introduction to sample space probability

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. In this article we shall discuss about probability sample space.(source: wikipedia)

Example Problem on Sample Space Probability

Example 1:

List the sample space in tossing a fair coin

Solution:

In tossing fair coin there are two possible outcomes namely head and tail

Hence the sample space in this experiment is given by

S= {H, T}

Example 2:

List the sample space in simultaneous toss of a tie and coin

Solution:

Clearly the sample space is given by

S= { ( 1, H), (2, H), (3,H), (4, H), (5, H), (6, H), (1, T) (2,T), (3 , T), (4, T), (5, T), (6, T)}

Example 3:

Two well balanced dice are rolled and the numbers that run turn up are observed. Determine the sample space

Solution:

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)}.

Example 4:

From a group of 2 boys and 3 girls, we select the two children what would be the sample space?

Solution:

Let us assume the boys as B1 and B2 and the girls as G1, G2 and G3. Then

S= {B1B2, B1G1, B1G2, B1G3, B2G1, B2G2, B2G3, G1G2, G1G3, G2G3}

Practice Problem on Sample Space Probability

Problem 1:

A coin is tossed twice if the second throw result in a tail then a die is thrown. Describe the sample space

Problem 2:

A bag contains 4 identical red ball and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of experiment?

by: jeri

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