All or nothing

Every now and again in school, usually before we’d adequately absorbed the last concept, our math teachers would announce a new segment of study.

“Monday, we will start working on probability,” Mr. Dial said.

I barely suppressed the groan that began in my toes and threatened to knock me out of my seat. Chances were if I were unsuccessful, Mr. Dial would knock me out. Probability, for crying out loud. Couldn’t they be a little more inventive?

For those of you who may have forgotten what I’m talking about, whether accidentally or deliberately, here are a couple of examples to refresh your memory of the types of questions we used to face when working probability problems.

1. You have 16 socks in a dresser drawer. Twelve socks are red; four are blue. You are dressing in the dark. How many socks will you have to remove from the drawer in order to get a matching pair?

2. You are rapidly approaching the Thruway tollbooth. You have eight quarters and eight nickels in your ashtray. How many coins will you have to pick out of the ashtray while careening down the off ramp in order to mete out 60 cents in exact change?

3. You have 40 pens in your backpack. There are 15 black pens, 15 blue pens, six red pens, two green pens, one pink pen and one purple pen. You need a pen to endorse a check. How many pens will you have to draw in order to sign your check in blue or black ink?

4. You are carrying two cans of soda and drop one of them. On your way to the car, you forget which one you dropped. What is the probability you will open the shaken one?

There are only two answers to questions of probability in my life: Probably and probably not. Mr. Dial wouldn’t have liked those answers, but at least the new state assessments allow students to explain how they arrive at an answer. Maybe I would get some points that way. In any event, here are my answers to the above questions.

1. I don’t throw loose socks in my drawer because I actually DO get dressed in the dark quite often. Whatever pair I draw, however, will not match what I plan to wear. In fact, they probably won’t match anything I own.

2. I am the only person who, in this situation, will draw all eight of one denomination. Might as well accept it and pull over before I get to the booth.

3. This one’s easy. The answer is 41. I will grab all the red, green, pink and purple pens before getting to the blue and black ones, which all will be out of ink. The 41st pen is the one I borrow from the teller. I will have to play the game again later, as there will be no handy waste receptacle to toss out the inkless wonders.

4. Some probabilities are really absolutes. I will arrive at work drenched in soft drink because I am wearing my last pair of matching socks, I am on the way to cash my check to have money for the toll operator and I have 40 pens to try before finding one that will work.

The most important thing I learned in studying probability was not to gamble. Not with my history. Murphy’s Law trumps anything mathematicians can dream up.

Reprinted courtesy Eagle Newspapers, Syracuse, New York.