Basic HTML Version
© 2014 Pacific Crest
119
3.1
Likelihood
P
urpose
The role this topic plays in quantitative reasoning
Wouldn’t you like to know if something is going to turn out they way you wanted or expected? When
looking at things like weather phenomena, medical treatment plans, stock market behavior, social
dynamics, sporting events, and political elections, wouldn’t you like to be able to differentiate between
the normal versus abnormal variation in the frequency of an event occurring?
Typical children about age 3 or 4 tend to ask if things are possible: “Could a hamster and a puppy be
friends? Could kitty fly if he ate a bird? Could the moon fall down?” are all the kinds of questions
young children ask. They soon discover that virtually nothing is impossible and that most things are
probabilistic. They pick up on patterns and begin using their own knowledge, experience, and predictions
to try and improve outcomes. Some children use what they discover to develop the quality of
persistence
,
negotiating probabilities with their parents or adults: “Can I have ice cream if I eat half my beans and all
my burger?” What children do is observe, generate, interpret, and report patterns for determining inter-
relationships and inter-dependences. Typical parental frustration should be lessened by appreciating the
cognitive development and sophistication on display in these kinds of interchanges!
The mathematical modeling of a life situation can be created with a set of trials of an experiment and
the identification of a specific event that models a decision or action and its outcome in real-life. The
mathematical modeling of a probabilistic system (Chapter 9) to determine the likelihood of an outcome
expands your ability to perform mathematical modeling where it is pertinent, both in your professional
and personal life. After this activity, you will question the nature, premises, and assumptions of models
that others present to you and those which you have chosen to use.
L
earning Goals
What you should learn while completing this activity
1. Model a probabilistic situation by identifying its outcomes and likelihoods.
2. Determine how likely an outcome of a specific event would be.
3. Analyze the appropriate use of likelihood calculations in existing mathematical models.
4. Translate the likelihood of an event occurring from percentages to language and visa versa.
D
iscovery
Finding out for yourself
Flip a coin 10 times and record the results. What is the likelihood that the pattern of heads and tails you
recorded would occur again? How does the likelihood of replicating that pattern compare to getting
heads 10 times in a row? What is the total number of different patterns that could occur when you flip the
coin 10 times? What is the likelihood of achieving, in any order, 2 heads and 8 tails in 10 flips of a coin?
Now explore the different likelihoods of causes of death.
W
hat Do You Already Know?
Tapping into your existing knowledge
1. In flipping a coin what is the likelihood (chance) of getting heads or tails?
2. When flipping a coin twice what is the likelihood of getting heads twice, tails twice, or one of each?