historical
- Jerome Cardan
- Laplace
- Blaise Pascal
- Fermat
the mathematics
probabilities range from 0 to 1.
- 0% will not occur - unlikely (impossible event has the probability of 0)
- 100 % is certain to occur - highly likely (certain event has the probability of 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.
- experimental
- theoretical
by experiment - durch ein Experiment
- number of trials - die Anzahl der Versuche
- outcomes - das Ergebnis
- frequency - die Häufigkeit
- relative frequency - die relative Häufigkeit
- estimated experimental probability -
- event - das Ereignis
investigations - Experimente
- coins (Münzen)
- dice (ein Würfel oder mehrere Würfel)
- spinners (eine Drehscheibe)
- selecting marbles form a bag (Urnen)
- cards form a pack (Spielkarten)
sample space - Ergebnisraum
set of all possible outcomes of an experiment. Die Menge aller möglichen Ergebnisse
Symbols used:
$\Omega$
- capital Greek letter Omega$U$
- for “universal” set
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
- event - das Ereignis
the theoretical probability of a particular event is the chance of that event occuring in any trial of the experiment.
- equally likely - gleich wahrscheinlich
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
links with interactive exercises
MEP CIMT
Aufgabenfuchs
Venn diagrams
with and without replacement - mit und ohne zurücklegen
conditional probability - bedingte Wahrscheinlichkeit
link to Sek II page