Probability

historical

the mathematics

probabilities range from 0 to 1.

in mathematics, we usually use fractions or decimals instead of percentages.

Note - in many German text books percentages are used.

You should be able to convert between fractions, decimal and percentages easily.

by experiment - durch ein Experiment

investigations - Experimente

sample space - Ergebnisraum

set of all possible outcomes of an experiment. Die Menge aller möglichen Ergebnisse

Symbols used:

event - das Ereignis

A set of outcomes of an experiment to which a probability is assigned. It is a subset (die Teilmenge) of the sample space.

example 1 - tossing one coin

$\Omega = \{H, T\} $

example 2 - tossing two coins

$\Omega = \{HH, TH, HT, TT\} $

2-dimensional grids

tree diagrams

example - tossing a coin (heads is event A) and rolling a 1 on a 4-sided dice (event B)

Note - in this example, the events are independent of each other. There is no conditional probability.

theoretical probability - Laplace-experiment

the theoretical probability of a particular event is the chance of that event occuring in any trial of the experiment.

complementary event

The complementary event A’ of an event A is the event that A does not happen.

The probability is calculated by

$$P(A') = 1 - P(A)$$

This is useful when one probability is less work to calculate.

grids - Vierfeldertafel

tree diagrams - Baumdiagram

rolling sixes with 3 dice

two coins

MEP CIMT

CIMT MEP - Probability

Aufgabenfuchs

Venn diagrams

with and without replacement - mit und ohne zurücklegen

conditional probability - bedingte Wahrscheinlichkeit

link to Sek II page

intro to binomial probability


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