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A
Successful Performance
Successful application of your learning looks like this
As you begin to apply what you’ve learned, you should have a good idea of what success looks like.
A SUCCESSFUL
PERFORMANCE
I determine the likelihood of an event for a defined situation. I...
●
Define
the problem correctly, including sample space, event space, and the likelihood of
outcomes
●
Validate that the event space likelihood is accurate
●
Use appropriate
terminology
when talking about likelihood
D
emonstrate Your Understanding
Apply it and show you know in context!
1. Think “Blackjack” or “Twenty-One!” Write the likelihoods of the events (12, 13, 14, 15, 16, 17, 18,
19, 20, or black jack) of the sample
space for a blackjack hand given that you haven’t looked at the card
that is face down, but the card showing is a 10 of diamonds and without seeing the dealer’s hand.
2. Betty and George have been married for 3 years and have decided they’re ready to try for their first
child. Assume that the chance, each month for the next five months of Betty getting pregnant is 5%, 10%,
15%, 10%, and 5% during the five days immediately surrounding ovulation but that due to hectic schedules,
they only have time for two trials during the time period and those trials are random during those days. They
continue this pattern for five months. What is the likelihood of Betty getting pregnant in each month?
3. You want to get three friends to go to a movie with you, and from past experience, you know that the
likelihood of a person saying they have a prior commitment increases by 10% per day. You start this
process 7 days in advance of the movie, but only have time to invite one person per day. There is a
70% chance that the first person you ask will say “Yes.” What does the likelihood look like for the
sample space of having the three people committed by day 3? What about by day 4, 5, 6, and 7?
4. You have four courses with two grading systems. The grading system for two of your courses range
from
A, B, C, W,
to an
F
. In your other two courses you can get either an
A, B, C, D, W
or
F
. As with most students you will want to achieve a certain level of collective performance for the
term: your GPA. Using the Methodology for determining likelihood: 1) Define the experiment, 2)
Outcomes of a trial, 3) Outcomes in the sample space, 4) Define the event you want, and 5) Define
the likelihood of achieving your expected grades (event).
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Model, the Methodology, and the Demonstrate Your Understanding (DYU) problem in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not. What is it that makes a problem
involving likelihood a difficult problem to solve?
What are the conditions and parameters that make a problem involving likelihood a difficult problem to
solve?
3.1 Likelihood