Friday, February 27, 2009

Possibilities vs. Probabilities

Citizens of the Junior High: The PSSAs are coming soon. That can only mean one thing:

Free breakfast.

You've probably heard the saying, "There's no such thing as a free lunch." Well, that's because there are way too many possibilities for breakfast.

Lets's consider the options you had for choosing your breakfast: Orange or apple juice (much to the dismay of Mathman, espresso isn't one of the options here) and a breakfast item of a Cocoa Puffs cereal bar, Trix cereal bar, cinnamon sugar donut, apple, banana, or the ubiquitous "Honey Bun".

If we were to quickly calculate the possibilities for the number of breakfasts we'd have:

Orange juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"

Apple juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"

So there are 12 possibilities for breakfast.

There's a simpler way of finding out how many ways to choose breakfast. Think about it 2 ways for juice, 6 breakfast items = 12 possibilities.

2 and 6 to get 12. Multiplication must be the secret operation.

Now, we can also consider that picking a juice doesn't effect the choice of a menu item. So choosing a juice and a breakfast item are independent events.

Now that we have considered the possibilities, let's consider the probability of choosing a particular breakfast. Let's look for P(apple juice, Trix cereal bar). The P() stands for probability of what's in the (). The P(apple juice, Trix cereal bar) is 1 result of 12 possibilities or a 1/12 chance. We could also get here by taking the P(apple juice)= 1/2 and P(Trix cereal bar) = 1/6. Once again, use the secret operation of multiply to get 1/12.

So the odds of getting Mathman's favorite breakfast of espresso and chocolate chip and banana pancakes is P(espresso, banana pancakes) = 0*0 = 0 since the P(espresso)=0 and the P(banana pancakes)=0.

Let's end on a positive note: the P(staying radical)= 1 or 100%. That's the only way to be.

Thursday, February 26, 2009

It's All in the Merchandising

Introducing our new weapon in the fight against ignorance:



Welcome the Algebratz.

I've read the PSSA manuals. I see nothing against using the Algebratz.

Thursday, February 19, 2009

You Probably Should Read Closely

Greetings citizens of the Junior High. It has recently come to my attention that many of you are slightly confused about two types of probabilities- theoretical and experimental. Well, I'd like to help you figure out the difference between the two.

First up: theoretical probability. This is simply an educated guess at what will happen in a situation. For instance, the theoretical probability that citizens of the Junior High will wash their hands after using the restroom to help prevent the spread of the "stomach flu" is 1 or 1/1 or 100%. It should be a sure thing, especially since there are signs stenciled on the walls that say "Please Flush" and "Please Wash Hands". You can refer to this probability as P(washing hands). Simple hand washing after using the restroom can limit the spread of the "stomach flu", which really isn't a flu at all, but often an e. coli bacterial outbreak.

In essence, a theoretical probability is just a hopeful prediction.

Now, we'll take a look at an experimental probability. This type of probability is a ratio based on the number of favorable outcomes out of the total number of trials. Quite simply, we conduct an experiment and observe what happens. For our example, if we notice that the water ran 5 times for 8 people leaving the restroom we can conclude that the experimental probability is 5/8 = 5 out of 8 = .625 = 62.5% of the people using the restroom washed their hands.

In many cases the theoretical and experimental probabilities are not equal. Often times the experimental probability is greater than the theoretical probability.

Unfortunately, in our example, the best we can hope for is that the experimental probability matches the theoretical probability. Especially since everyone can read the writing on the wall- "Please Wash Hands".

We are not even going into theoretical and experimental probabilities of the "Please Flush" signage.

Citizens of the Junior High, remember: Only you can wash your hands.

Tuesday, February 17, 2009

Pick a Winner?

Dear Mathman,

My friends and I are starting a chapter on probability. We were wondering, Do you pick your nose?

Sincerely,
Laura



Dear Laura,

I'm not sure exactly what you are referring to by "Do you pick your nose?" It sounds like this sentence is in the present tense and an ongoing process, so I'd have to say the answer is "No.", as I didn't have any kind of option in choosing my nose. BUT, If I indeed did have several equally likely noses to choose from- let's say 4, the odds I would have chosen my current nose are 1 in 4 = 1/4 = .25 = 25%.

Life is full of choices; You can pick your friends but you can't pick your nose.

Stay radical,
Mathman

Wednesday, February 11, 2009

Don't Leave Math Behind.

We use language everyday. As great as words are though, they sometimes get put into sayings that have different meanings. For instance: "Cool" could refer to temperature, or it could refer to something that is "Groovy", "Awesome", or even "Radical". This makes English a bit confusing to someone who has the capability to time travel.

Language is great, however, because without it we wouldn't be able to ask such timeless questions as "Why did the chicken cross the road?" or "What were you thinking?" We also wouldn't be able to make such statements as "I'm hungry." or "Employees must wash hands before returning to work."

Recently, language has been compacted by the phenomenon known as texting. LOL. BFF. FAQ. These acronyms are so common the most people know their meanings immediately and don't have to think about what they mean.

That's great and all, but that leaves math out of the equation for the most part. I mean, if English gets texting, shouldn't math get digiting? It's not really fair that they get all the abbreviations when we're stuck with + for add, - for subtract, x for multiply, and / for divide. That's sooooo middle ages.

It's time, citizens of the Junior High, to start bringing math back into the 21st century.

Announcing our new acronym: (drum roll please) SIF

Do you know what it stands for? How about: Slope-Intercept Form. What is Slope-Intercept Form you ask? It's a form you fill out that has the slope and the y-intercept in it. It's the same form ALL the time, just the slope and intercept get filled in.

SIF: y=mx+b, where m is the slope (rise over run) and b is the y- intercept, the place where the graph crosses the y-axis.

Say it with me:SIF.

Stay radical, or at least keep being a regular quadrilateral.

Tuesday, February 3, 2009

Valentine's Day Question for the All Knowing Mathman!!!

Dear Mathman,

I have a major problem and I need your help. With Valentine’s Day quickly approaching, I have this special someone that I need a gift for. I am not the romantic but I want to do something special, so I need some suggestions of what to get. Let me know if you have any thoughts.

Thanks,

Cupid





Dear Cupid,

I have the same problem. What do you buy that special someone to show her/him that you really care? Here are some great ideas that have gotten me out of some tough problems.

Ruler, compass, protractor, a slide rule, up-to-date formula sheet, scientific calculator with fraction button and directions (great to help on the PSSA test), but the one gift that will really show you care is a pass to Math Help at the BJHS every Tuesday and Thursday. The gift of knowledge cannot be replaced. It is a gift for that special someone to continually grow. With this gift, the person’s love will continue to grow exponentially. A solid base/foundation is important with everything especially in math. I encourage everyone to give this special gift to everyone.

Thanks,

Mathman