A Brief Description of Experimental probability

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NEO Fri, Feb 04, 2022 11:19 AM UTC

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 (𝑬𝑬) happening.
For any event we can assign a number between 𝟎𝟎 and 𝟏𝟏 to describe the likelihood that it will occur.
An impossible event has a probability of 𝟎𝟎. A certain event has a probability of 𝟏𝟏. All other events between
these extremes can be assigned a probability between 𝟎𝟎 and 𝟏𝟏.
A number line can be used to represent different probabilities:
Very unlikely to happen Very likely to happen
0 ½ 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 ½, 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(ℎ𝑒𝑒𝑒𝑒𝑒𝑒) =
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 ½.
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.
𝒏𝒏𝒏𝒏. 𝒐𝒐𝒐𝒐 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒂𝒂𝒂𝒂 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐 𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅 𝒂𝒂𝒂𝒂 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆
𝐩𝐩 𝑬𝑬 =
𝒕𝒕𝒕𝒕𝒕𝒕 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒏𝒏𝒏𝒏. 𝒐𝒐𝒐𝒐 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒕𝒕𝒕𝒕𝒕𝒕 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 𝒘𝒘𝒘𝒘𝒘𝒘 𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄
Experimental probability 10/2013 © SLC 1 of 2

2. Learning
Centre
EXAMPLE 1
On one day Ben’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:
𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 6 2
p 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = = =
𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 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 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 6 3
p 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = = =
German shepherds 6 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 14 7
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Experimental probability 10/2013 © SLC 2 of 2

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