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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 randomness a difficult problem to solve?
What are the conditions and parameters that make a problem involving randomness a difficult problem
to solve?
T
roubleshooting
Find the error and correct it!
Identify the error and provide a correction:
A bookie is taking bets on the 2014 NBA Championship: Miami Heat vs. San Antonio Spurs. Dan
and Lou decided to pool their funds and go for it.
Dan pointed out that the Miami Heat beat the Spurs last year, coming from behind by 5 points with
31 seconds to go; they overcame a 3-2 deficit! But not only that, they won in game seven.
Lou countered that San Antonio has the home court advantage, that they won more games, have
played more difficult teams, and have won by a larger average of points.
Dan said that Miami has the best player in the world, the confidence of beating San Antonio last year
and a healthy Dewayne Wade on their side.
The friends agreed that the key factors are: home court advantage, playoff experience, best player,
and coach. They even agreed in the ranking of factors: home court, best player, coaching, depth, and
confidence.
A San Antonio newspaper predicted one upset on each team’s home court (Spurs and Heat), and
that as long as there is not a second upset, the smart money is on San Antonio having a 58% chance
of winning the championship. A Miami newspaper predicted that the Miami Heat could run off 4
straight victories (they’d done it before, after all) and that it was very unlikely that San Antonio
could put Miami away in anything short of 6 or 7 games.
All things considered, Dan and Lou agreed to bet on the hungry nature of San Antonio’s team and
that neither of them liked Miami, both having visited in the last several years.
M
aking it Matter
Solving problems in your life
●
Assume that you’ve been asked to help a friend calculate how to increase the odds of finding a
worthwhile summer job. Use the methodology to figure out how to reduce randomness in this
challenge.
●
Reduce randomness to model driving safety: Explore the factors that lead to accidents and use the
methodology to suggest ways to reduce traffic accidents when you are driving. What are the most
significant factors that lead to accidents and how can you remove the of those factors occurring?
3.2 Finding Patterns in Random Behavior