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13-1 Experimental and Theoretical Probability

12-7
Experimental and
Theoretical
Probability
Outcome: the result of a single trial,
such as spinning a wheel
Event: any outcome or group of
outcomes
Sample space: the set of all possible
outcomes
Theoretical Probability: describes the
likelihood of an event based on
mathematical reasoning
𝑃 𝑒𝑣𝑒𝑛𝑑
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
=
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
Problem 1: Finding Theoretical Probability
Our solar system’s 8 planets, in order of
least to greatest distance from the sun, are
Mercury, Venus, Earth, Mars, Jupiter,
Saturn, Uranus, and Neptune. You will
randomly draw one of the names of the
planets and write a report on that planet.
What is the theoretical probability that you
will select a planet whose distance from
the sun is less than Earth’s?
Complement of an event: consists of
all of the possible outcomes in the
sample space that are NOT part of the
event
𝑃 π‘›π‘œπ‘‘ 𝑒𝑣𝑒𝑛𝑑 = 1 βˆ’ 𝑃(𝑒𝑣𝑒𝑛𝑑)
𝑃 π‘›π‘œπ‘‘ 𝑒𝑣𝑒𝑛𝑑
# π‘œπ‘“ 𝑒𝑣𝑒𝑛𝑑𝑠 π‘‘β„Žπ‘Žπ‘‘ π‘Žπ‘Ÿπ‘’ π‘›π‘œπ‘‘ 𝑒𝑣𝑒𝑛𝑑
=
π‘‘π‘œπ‘‘π‘Žπ‘™ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
Problem 2: Finding the Probability of the
Complement of an Event
A jar contains 10 red marbles, 8 green
marbles, 5 blue marbles, and 6 white
marbles. What is the probability that a
randomly selected marble is NOT green?
Odds: describe the likelihood of an event as a
ratio comparing the number of favorable and
unfavorable outcomes
π‘œπ‘‘π‘‘π‘  𝑖𝑛 π‘“π‘Žπ‘£π‘œπ‘Ÿ
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
=
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘’π‘›π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
π‘œπ‘‘π‘‘π‘  π‘Žπ‘”π‘Žπ‘–π‘›π‘ π‘‘
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘’π‘›π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
=
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
Problem 3: Finding Odds
What are the odds in favor of
the spinner landing on a
number greater than or equal
to 6?
What are the odds against the
spinner landing on a number
less than 3?
Experimental Probability: measures the
likelihood that the event occurs based on the
ACTUAL results of an experiment
𝑃 𝑒𝑣𝑒𝑛𝑑
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘‘π‘–π‘šπ‘’π‘  π‘‘β„Žπ‘’ 𝑒𝑣𝑒𝑛𝑑 π‘œπ‘π‘π‘’π‘Ÿπ‘ 
=
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘‘π‘–π‘šπ‘’π‘  π‘‘β„Žπ‘’ 𝑒π‘₯π‘π‘’π‘Ÿπ‘–π‘šπ‘’π‘›π‘‘ 𝑖𝑠 π‘‘π‘œπ‘›π‘’
Problem 4: Finding Experimental
Probability
A quality control inspector samples 500
LCD monitors and find defects in three of
them
What is the experimental probability that a
monitor selected at random will have a
defect?
Problem 5: Using Experimental Probability
You ask 500 randomly selected households in
your town if they have a dog. Of the 500
households, 197 respond that they do have a
dog. If your town has 24,800 households, about
how many households are likely to have a dog?

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