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Section 4.1
Classical Probability
HAWKES LEARNING SYSTEMS
Probability, Randomness, and Uncertainty
math courseware specialists
4.1 Classical Probability
Definitions:
• Probability experiment – any process in
which the result is random in nature.
• Outcome – each individual result that is
possible for a given experiment.
• Sample space – the set of all possible
outcomes for a given experiment.
• Event – a subset of the sample space.
HAWKES LEARNING SYSTEMS
Probability, Randomness, and Uncertainty
math courseware specialists
4.1 Classical Probability
Sample space and events:
Consider an experiment in which a coin is tossed
and then a 6-sided die is rolled.
a. List the sample space for the experiment.
b. List the outcomes in the event “tossing a tail then rolling
an odd number”.
Solution:
a. Each outcome consists of a coin toss and a die roll.
b. Choosing the members of the sample space which
fit the event “tossing a tail then rolling an odd
number” gives:
{T1, T3, T5}
HAWKES LEARNING SYSTEMS
Probability, Randomness, and Uncertainty
math courseware specialists
4.1 Classical Probability
Three methods for calculating the probability:
1. Subjective – an educated guess regarding
the chance that an event will occur.
2. Empirical – if all outcomes are based on
experiment.
3. Classical – if all outcomes are equally likely.
HAWKES LEARNING SYSTEMS
Probability, Randomness, and Uncertainty
math courseware specialists
4.1 Classical Probability
Determine whether each of the following probabilities is
subjective, empirical, or classical:
a. The probability of selecting the queen of spades out of
a standard deck of cards. (1 out of 52 cards).
Classical
b. An economist predicts a 20% chance that technology
stocks will decrease in value over the next year.
Subjective
c. A police officer wishes to know the probability that a
driver, chosen at random, will be driving under the
influence of alcohol on a Friday night. At a roadblock,
he records the number of drivers and the number of
drivers driving with more than the legal blood alcohol
limit. He determines that the probability is 3%.
Empirical
HAWKES LEARNING SYSTEMS
Probability, Randomness, and Uncertainty
math courseware specialists
4.1 Classical Probability
Calculate the probability:
A large jar contains more marbles than you are willing
to count. Instead, you draw some coins at random,
replacing each coin before the next draw. You record
the picks in the following table:
Red
Blue
Green
Yellow
Purple
15
29
25
31
10
a. What is the probability that on your next draw you
will obtain a blue marble?
b. What is the probability that on your next draw you
will obtain a yellow marble?
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4 out of 6, thus 2 out of 3
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Total = 44 + 57 + 77 = 178
Total = 44 + 49 + 23 + 37 + 22 = 175
The probability that will be an ace is 4/52
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Number of outcomes = 6 results to the power of 2 pairs = 62 = 36
Number of Events (sum of 10) = 5 and 5, 4 and 6, 6 and 4 = 3
Probability (sum of 10) = 3/36 = 1/12
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Number of outcomes = 2 results to the power of 8 tosses = 28 = 256
Number of Events (all tails) = T T T T T T T T = just once = 1
Probability (all tails) = 1/256
Click “/” to add denominator
Number of chips above 111 = 434 – 111 = 323
Probability (above 111) = 323/434