# A Brief Description of Experimental probability

Contributed by:
This pdf includes the following topics:-
Theoretical Probability
Experimental Probability
Examples and many more.
1. Learning Experimental
Centre Probability
Theoretical Probability: what should occur mathematically in an experiment.
Experimental Probability: what actually occurs when the experiment is carried out.
Probability (p) is the mathematics of chance. Probability tells us the likelihood of an event (π¬π¬) happening.
For any event we can assign a number between ππ and ππ to describe the likelihood that it will occur.
An impossible event has a probability of ππ. A certain event has a probability of ππ. All other events between
these extremes can be assigned a probability between ππ and ππ.
A number line can be used to represent different probabilities:
Very unlikely to happen Very likely to happen
0 Β½ 1
Not likely to happen Likely to happen
Impossible Equal chance of happening or not Certain
For example, the probability of getting a head if you flip a coin is Β½, since only 2 things
could happen (a head or a tail) and each one has an equal chance of occurring.
Experimental probabilities are those you calculate by actually carrying out an
experiment (like flipping a coin). An example would be to flip a coin 40 times and
record whether you get a head or a tail. After 40 tosses of the coin calculate the
experimental probability of obtaining a head by recording the number of heads that
occurred as a fraction of the total number of tosses.
23
Applying the formula above we get: p(βππππππ) =
40
If we repeated this experiment a very large number of times then the experimental
probability of obtaining a head would get very close to the theoretical probability of Β½.
The experimental probability of an event occurring is the number of times that it
occurred when the experiment was conducted as a fraction of the total number of
times the experiment was conducted.
ππππ. ππππ ππππππππππ ππππ ππππππππππ ππππππππππππππ ππππππππππππ ππππ ππππππππππππππππππππ
ππππππ ππππππππππ ππππ. ππππ ππππππππππ ππππππ ππππππππππππππππππππ ππππππ ππππππππππππππππππ
Experimental probability 10/2013 Β© SLC 1 of 2
2. Learning
Centre
EXAMPLE 1
On one day Benβs Bagel Shop sold 15 bagels, of which 6 were raisin bagels. Use experimental
probability to predict what fraction of his sales will be raisin bagel the next day. Hint: always write the
experimental probability as a fraction in simple form, using the following formula:
ππππππππππππ ππππ ππππππππππππ ππππππππππππ π π π π π π π π  6 2
p ππππππππππππ ππππππππππ = = =
π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘ ππππππππππππ ππππ ππππππππππππ π π π π π π π π  15 5
EXAMPLE 2
There were dogs of many different breeds at the dog park last Saturday. Use experimental probability to
determine that a dog picked at random in the neighborhood will be a German Shepherd.
Yorkshire terriers 3
Springer spaniels 3
Dachshunds 1 ππππππππππππ ππππ ππππππππππππ π π π π π π π π π π π π π π π π  6 3
p ππππππππππππ π π π π π π π π π π π π π π  = = =
German shepherds 6 π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘ ππππππππππππ ππππ ππππππππ 14 7
STUDENT LEARNING CENTRE
REGISTRY BUILDING ANNEXE
TEL: 61-8-8201 2518
E-MAIL: [email protected]
INTERNET: http://www.flinders.edu.au/SLC
POSTAL: PO BOX 2100, ADELAIDE, SA 5001
Experimental probability 10/2013 Β© SLC 2 of 2