5: Basic Concepts of Probability
- Page ID
- 4803
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
Learning Objectives
Develop the students:
- ability to do the counting
- probabilistic reasoning
Thinking out Loud
What do we mean if we say that the probability of tossing a coin and seeing a head is about 0.5 (50% or the odds are 50/50)?
One possible answer: We are claiming that if you toss the coin in question a large number of times then you should see heads appearing about half of the time.
Thinking out loud
What do people mean when they refer to a "100-year" flood?
One possible answer: They are claiming that the likelihood of a flood of that magnitude happening in any given year is 0.01 (1%, or the odds are 1/100).
- 5.1: Counting
- Most of us think that counting is easy is 1,2,3.... When counting objects, one needs to careful on not counting more than once and missing an objects. In this section, we explore some ideas behind counting.
- 5.2: Probability: Living with odds
- Probability is a subtle concept: There are several different things we mean by probable. Our knowledge of things to come is imperfect. What can we say in the face of imperfect knowledge? How can we reason knowing our knowledge is imperfect
Contributor
Pamini Thangarajah (Mount Royal University, Calgary, Alberta, Canada)