Probability Explanation And Exercises Worksheet Page 5
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37Basic Concepts
by David M. Lane
Prerequisites
• Chapter 5: Introduction to Probability
Learning Objectives
1. Compute probability in a situation where there are equally-likely outcomes
2. Apply concepts to cards and dice
3. Compute the probability of two independent events both occurring
4. Compute the probability of either of two independent events occurring
5. Do problems that involve conditional probabilities
6. Compute the probability that in a room of N people, at least two share a
birthday
7. Describe the gambler’s fallacy
Probability of a Single Event
If you roll a six-sided die, there are six possible outcomes, and each of these
outcomes is equally likely. A six is as likely to come up as a three, and likewise for
the other four sides of the die. What, then, is the probability that a one will come
up? Since there are six possible outcomes, the probability is 1/6. What is the
probability that either a one or a six will come up? The two outcomes about which
we are concerned (a one or a six coming up) are called favorable outcomes. Given
Basic&Concepts&
that all outcomes are equally likely, we can compute the probability of a one or a
six using the formula:
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In this case there are two favorable outcomes and six possible outcomes. So the
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probability of throwing either a one or six is 1/3. Don't be misled by our use of the
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term “favorable,” by the way. You should understand it in the sense of “favorable
to the event in question happening.” That event might not be favorable to your
P(6!or!head)!=!P(6)!+!P(head)!.!P(6!and!head)!
well-being. You might be betting on a three, for example.
!!!!!!!!!!!!!=!(1/6)!+!(1/2)!.!(1/6)(1/2)!
!!!!!!!!!!!!!=!7/12!
189
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