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Introduction to Probability

Introduction to Probability

Author: Samsam Warsame

In this learning packet you will learn new terms and definitions, have an introduction of common terms in probability, and examples of how they are used. Lastly, there will be a demonstration of the rules of probability.



Since you will be introduced to the topic of probability, it is recommended at this point that you know general statistical terminology. However, some new terms you will learn are Probability of an Event, Outcome, Sample Space, Sample Points, Event, Mutually Exclusive, All Inclusive, and With Replacement vs. Without Replacement.

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Extra Problems

Please try to Work out these Extra Problems for Practice.

If you do not understand how to solve these problems, please refer to the learning packet (above),

--or the websites that I have cited (summary box).

Answers are given in the text box below!


Example 1: With Replacement

What is the probability of tossing a fair coin twice in a row and getting heads both times?


Example 2: Without Replacement

If you draw two cards from the deck without replacement, what is the probability that they will both be aces?


Example 3: List out the outcomes, probability of events, whether its mutually exclusive or all inclusive, sample space, and sample points


A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? of rolling an odd number?


Probabilities of Events:

Mutually Exclusive/All Inclusive:

Sample Space:

Sample Points:


Example 4: Events

Suppose we draw a card from a deck of playing cards. What is the probability that we draw a spade?




Answers to Examples

Example 1: With Replacement

 Answer: Since the probability of tossing a head (independent events) is 1/2 each time P(HH) = (1/2)(1/2) = 1/4.


Example 2: Without Replacement

 Answer:  P(AA) = (4/52)(3/51) = 1/221.



Example 3:


Outcome: The possible outcomes of this experiment are 1, 2, 3, 4, 5 and 6.

Probabilities of Events:

P(1) = # of ways to roll a 1 = 1

              total # of sides        6

P(2) = # of ways to roll a 2 = 1

              total # of sides        6

P(3) = # of ways to roll a 3 = 1

              total # of sides        6

P(4) = # of ways to roll a 4 = 1

              total # of sides        6

P(5) = # of ways to roll a 5 = 1

              total # of sides        6

P(6) = # of ways to roll a 6 = 1

              total # of sides        6


Mutually Exclusive or All Inclusive: Mutally Exclusive

(since only one number can appear on the top of the dice)

Sample Space: S= {1,2,3,4,5,6}

Sample Points: The sample points are 1,2,3,4,5,6

or this experiement has 6 sample points


Example 4: Events

 Answer: The sample space of this experiment consists of 52 cards, and the probability of each sample point is 1/52. Since there are 13 spades in the deck, the probability of drawing a spade is

P(Spade) = (13)(1/52) = 1/4