Download Intro to Probability

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Percentages
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Write the percent as a decimal.
54%

Write the decimal as a percent.
0.00004
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Write the fraction as a percent.
3/8
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GOAL: Determine theoretical and experimental probability.

What are some characteristics of dice?

Sample space is the set of all possible outcomes
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example: When rolling a 6-sided die, the possible outcomes
are:
{1,2,3,4,5,6}
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Theoretical Probability can be used when a sample space
has equally likely outcomes, and we know it for a fact
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example: Each side is ___________ likely when rolling a sixsided die.
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When an event A occurs in m of the possible n outcomes,
𝑃 𝐴 =
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example: The probability of rolling a 3 with a six-sided die is:
𝑃 3 =
Theoretical Probability with Coins

Find the probability of a coin landing on tails.
Theoretical Probability with Cards

Find the probability of choosing a queen when randomly
selecting a playing card from a standard deck.
Biology Connection
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In genes, there are dominant (G) and recessive (g) traits. Each person
carries 2 traits. If at least one trait is dominant (GG or Gg), then the
person portrays that trait. Only if both are recessive (gg) does the
person portray the recessive trait. When a parent has both a dominant
and a recessive gene, then the two genes are equally likely to be
passed to a child.
Immunity to poison ivy is a dominant trait. Suppose that a child has two
parents who both have just one dominant poison ivy immunity gene.
What is the theoretical probability that the child will be immune?
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Choose one of the following:
1
2 3
4

Conditions:
Value
1
2
3
4
# of occurences
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Experimental Probability can be used when we don’t have
equally likely outcomes, but instead we have a collection of
trials
number of times the event occurs
total number of trials

𝑃 event =
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example: The probability of choosing a 3 based on our
experiment is:
Value
# of occurences
1
2
3
4
Experimental Probability with Sports

When the University of Texas won college football’s national
championship in the 2006 Rose Bowl game, its
quarterback completed 30 of 40 passes. Find the
experimental probability of the quarterback completing a
pass.
Experimental Probability with Fish

A pond contains three types of fish: bluegills, red gills, and
crappies. Each fish in the pond is equally likely to be
caught. You catch 120 fish and record the type. Each time,
you release the fish back into the pond. The frequency
distribution shows your results. If you catch another fish,
what is the probability that it will be a bluegill?
Fish Type
Number of times caught, f
Bluegill
39
Red gill
51
Crappy
30
Total = 120
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If actual trials are difficult to conduct, you can find
experimental probabilities by using a simulation, or a model
of one or more events.
Experimental Probability with a Simulation
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Suppose you take a true-or-false quiz and guess for
answers at random. What is an experimental probability
that you will get at least three answers correct?

15 trials
Digits:
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o 0-4 correct
o 5-9 incorrect
Geometric Probability

Suppose that all the points on the circular dartboard shown
below are equally likely to be hit by a dart you have thrown.
Find the probability of scoring at least ten points, given that
the dart lands somewhere within the area of the dartboard.
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Is this theoretical or experimental?
Venn Diagram Probability
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In a class of 147 students, 95 are taking math, 73 are
taking science, and 52 are taking both math and science.
One student is picked at random. Find each probability.
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P(taking science)
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P(not taking math)
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P(taking neither math nor science)
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Is this theoretical or experimental?
M
S
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In a town of 50 people, 40 own cats, 18 own dogs, and 12
own cats and dogs. If one person is randomly selected,
what is the probability that he/she owns a cat and not a
dog?
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Create a Venn diagram to assist.
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What is the difference between theoretical and
experimental probability?