Maybe, It's Impossible? For Sure. No, it's not! *
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It's Impossible
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Probability and Statistics (Which Mos Def raps about--below!)
Directions:
Some things are sure to happen. If today is Monday, tomorrow will be Tuesday. Some things are impossible. You can't roll a seven with only one of a pair of dice. Some things may or may not happen. Maybe it will snow, maybe it won't.
With each of the following statements, choose "Must be!," when something is for sure; "Maybe, maybe not," when something might be true; or "Impossible!" when something is absolutely impossible!
-
???
There is a live dinosaur in the zoo. -
???
You will get tails if you toss a coin. -
???
It will rain on Saturday. -
???
Superman will always beat the bad guys. -
???
The next time you throw an ordinary ball, it will keep going up into space. -
???
Someone will win a state lottery twice in one year. -
???
When you grow up, you will be ten feet tall. -
???
Outdoors at night you can see the stars in the sky. ???
Your Little League team will win its next game.-
???
The earth revolves around the sun. -
???
You will be in school tomorrow. -
???
In a new box of crayons, at least one will be red.
* * *
Does everyone agree on which things are for sure and which are not? (Careful! It's o.k. to disagree, but standardized tests are built around the idea of right and wrong answers. Thus the test creators may make some arbitrary decisions about what is impossible and what is not, so when you get to the tests, forget about debating anything; you have to decide what answer is the best in most people's and educators' minds.)
Should everyone agree?
Why or why not?
Explore other topics such as:
- Chance of Rolling Two Sixes;
People With the Same Birthday:
Calculating Probability
- Sampling and Probability:
- colors in a jar: make a collection of colored pencils or papers or m&m's, place in a jar, and have friends 'sample' some of the jar's contents to guess the percentage of each color!
- letters in the alphabet: which letters are the most commonly used in English? 'Sample' different texts you find and see? How many texts do you need to sample until you think to have a good idea of the most commonly used letters? Are there any kinds of texts you should sample?
- Scientists and sampling (calculate: total fish in a pond; the population of the U.S.; or--using opinion polls--Presidential outcomes)
Links
- Robert Todd Carroll, "Gambler's Fallacy" in The Skeptic's Dictionary (http://skepdic.com/gamblers.html). With notes on playing State Lotteries and "Gambler's Fallacy." (Note that some people do disagree as to whether past events influence the likeliness of future ones; for example, if I throw a penny three times and each time get tails, does this mean the penny will come up heads on the fourth toss, because the heads and tails have to eventually even out according to probability? Or does it mean that it will probably come up tails on the fourth toss [probably thanks to something about the way I toss this particular penny]? Or do the outcomes of my previous tosses not affect the probability of the forth toss's yielding either heads or tails [thus leaving a 50-50 chance of getting either heads or tails on the fourth toss]? You are free to disagree about this -- except again, not on standardized exams! [Of course, if you are calculating the probability for a whole collection of events, and the probability for the events in the collection is calculated all at once, as a single probability, then, if the odds are fifty-fifty of something's happening under a certain set of circumstances, and you have ten such circumstances in a collection, you can probably safely guess that in five out of those ten times, that something will happen.])
- Probality (http://brainyplanet.com/index.php/ProbabilityProblems?PHPSESSID=db3b9d9c944cddaf0d9060ac8f57f493 ), part of: Recreational puzzles.org (Usenet rec.puzzles)(http://rec-puzzles.org/)
- Monster and Me (A game; in it there are options to play with slot machines and bet with dice!) (http://www.monsterandme.com/1about/attach2.htm)
- Alexander Bogolmony: Cut-the-knot: Probability and Probability Problems(http://www.cut-the-knot.com/probability.shtml)
- Math Forum: The Beginnings of Probability(http://www.mathforum.org/isaac/problems/prob1.html)
- Another cut-the-knot site: cut-the-knot.org (a bit more abstract look at math and probability, but some of the problems will appeal)--
Highlights Below
- Probability ( http://www.cut-the-knot.org/probability.shtml )
- Birthday Coincidence ( http://www.cut-the-knot.org/do_you_know/coincidence.shtml) Note: this is a place to explore the chances of two people's having the same birthday!
- Probability of Lying (
http://www.cut-the-knot.org/Probability/FalseWitness.shtml)
(Do you want a clue as to how to approach this problem? See Solving Cut-the-knot's "Unreliable Witness".) - Careless Mailing Clerk ( http://www.cut-the-knot.org/Probability/TenLetters.shtml)
- Prisoners Communicating Via a Single Light Bulb (
http://www.cut-the-knot.org/Probability/LightBulbs.shtml )
Note: this problem is tough to solve, mathematically, and also emotionally. (Why are the prisoners there? One might wonder, what did they do?-- because there are multiple ways to solve this problem: if you solve it one way, you must risk the lives of the prisoners--and declare they have all been in the room when it is uncertain but probable; if you're right, they will be liberated; if you solve it another way, you do not risk any lives, for you have a system that enables you to be certain--if you get to a certain point--that all prisoners have been in the room; but there is a possibility that you will never get to that point. For either solution, and especially for the second, which requires all or nearly all prisoners to see the lightbulb change many times, patience is essential throughout the process, and the solution will thus take a good deal of time. But maybe the prisoners are criminals and deserve to be where they are? Perhaps, but to understand more about the other kind of prisoners, read more about Elie Weisel's book about being imprisoned during the Holocaust, Night. )
[Click when you are done reading about the Lightbulb Problem!] - Tips for Playing at Pegs (
http://www.cut-the-knot.org/proofs/pegsolitaire.shtml)
Note: This site does not seem to be quite about probability, but rather, about how to predict absolutley the outcomes of your moves!
- The Wizard of Odds: Strategies for Gamblers: Ask the Wizard (http://wizardofodds.com/askthewizard/numbered/askthewizard120.html)
- Probability, Odds of Winning Roulette after Various Numbers of Spins: Is There a Way To Get Ahead and Quit?
- The Two Faces of Gambling: A Seattle Post article(http://seattlepi.nwsource.com/local/face21.shtml)
- Mrs. Glosser's Math Goodies: Probability (http://seattlepi.nwsource.com/local/face21.shtml)
A good introduction; additional lessons must be purchased however! My favorite (free) pages here are: "Introduction" and "Independent Events"
* * *
- If you said that something must happen, is there any circumstance under which it might not happen?
- If you said that something may or may not happen, is it more or less likely to happen than other things which may or may not happen?
- Is there any way to predict at all how likely it is to happen?
- If you can predict it, how accurately can you predict it usually?
- If you said that something must not happen, is there any circumstance under which it might happen?
* * *
Activity Adapted From: Jean Cushman (1991), Do You Wanna Bet? Your Chance to Find Out About Probability, illustrated by Martha Weston (New York: Clarion Books): 18.
* * *
NASA Hubble Spotlight: The Importance of Math in Science
(http://www.youtube.com/watch?v=51FaaMZ3EBg)
(NOTE: women and minorities are especially underrepresented in the math and sciences fields!)
* * *
from Mos Def's "Mathematics" (at http://www.lyrics.net.ua/song/55131)
In this song, Mos Def raps about how the mathematics and statistics of poverty add up:
Young teens and prison greens facin life numbers
Crack mothers, crack babies and AIDS patients
Young bloods can't spell but they could rock you in PlayStation
This new math is whippin motherfuckers ass
You wanna know how to rhyme you better learn how to add
It's mathematics
[Solving Cut-the-knot's "Unreliable Witness."]