# Probability Faery Tales

/To wrap up our recent probability unit in Math Studies I had my students write their own probability problems. For review at the end of «covering the content» students got to select a few options from a menu of rather lame probability worksheets I dug out from the filing cabinet. After this I had the kids create their own probability worksheet. I set this up with Google Docs and it worked great. I will see if I can summarize the process clearly here:

- Students wrote their original problem and solved it.
- Students posted their problem on a common Google Doc and posted a link to their solution on a separate Google Doc (this was so that students could solve all the problems that were created without being distracted by the solutions. This was their idea not mine. It worked
- Students reviewed each others problems and solutions. They looked for possible mistakes, and offered feedback for improvement.
- As the kids did all of these tasks they filled out a table on top of the Google Doc with the problems on it, this helped keep everything organized.

Here are a few of the problems the kids came up with.

### Noah's Clever College Worksheet:

In a fraternity of 90 frat boys, 48 of them like sports, 45 of them like rap music, and 20 of them like to play Pepsi pong. 12 of the boys like to play sports and like rap music, 9 of the boys like to play Pepsi pong and play sports, and 2 of the boys like rap music and Pepsi pong. Surprisingly, no Frat boys partake in all activities.

One day the school dean became concerned with the level of safety of each of the boys and how many activities they were partaking in, so he decided to survey the level of intensity of each frat boy.

(A) Fill in the Venn Diagram

(B) How many Frat boys like all three activities?

(C ) How many Frat boys like only sports?

(D) How many Frat boys like only Pepsi pong?

(E) How many Frat boys don't participate in any activities?

(F) How many Frat boys only like rap music?

(G) How many Frat boys like only one activity?

This one was edited slightly for content but not where you would expect. This problem created lots of interesting debate in the discussion board before Noah added the line «Surprisingly, no Frat boys partake in all activities.»

### Nikita's Two Way Table Practice

One day Mr Roy walked into his room to find that the pillar in his room had been magically transformed into a hollow tree! When he walked inside, a voice (that may or may not have belonged to Gandalf) asked him to choose between a life-time supply or Petit Ecoliers, or Pepito’s. Of course, Mr Roy being the generous person that he is decided that he would ask his students which they would prefer so that he could share. Here are the final results of his survey:

Prequel: Knowing that Mr Roy surveyed 37 people, create you own Two Way Table.

(A) If one person was selected at random, find the probability that they love Petit Ecolier.

(B) If one person is randomly selected, find the probability that they hate Pepito

(C) If one person was selected at random, find the probability that they love both Pepito and Petit Ecolier (who can blame them?).

(D) If a person was randomly selected, find the probability that they hate Pepito or hate Petit Ecolier.

(E) If a person was selected at random, find the probability that they love Petit Ecolier, given that they love Pepito.

(F) Looking at Mr. Roy’s results, which were preferred: the Lu or the Pepito the winners?

I love this problem because it employs a two way table with conditional probability. And, of course, because Nikita littered it with references only our class could love. My classroom has a large column by the bookcase and occasionally we have discussed decorating it like a large tree. The students are also keen on hollowing it out into some sort of fort. (I try to remind them that this is a support column, but they will have none of it.) Nikita also mentions our recent discussions of the virtues of Lu's delicious Petit L'Ecolier biscuits and the new to me Pepito cookies. When I mentioned in class my affinity for Petit L'Ecoliers the students insisted I had to try the Pepitos and so they brought a bunch in. Pepitos (not available in the US I don't believe) are delicious as well!

Finally, Ben wrote a very snarky probability problem that involved my (most likely) demise at the hands of either the big bad wolf or the witch. I reworded the problem slightly, swapped Ben for myself and put it on their probability quiz.

### Ben's Walk In The Woods

Benjamin is walking along through the woods dodging Easter bunnies and flying carpets. After a while he came across a clearing, in the middle of which stood large house made out of gingerbread and covered with delicious treats like Pepito and Petit L’Ecolier biscuits. As he cautiously picked his way across the lawn made of treacle he heard a wolf give a howl of sweets. As he approached the door, an old woman opened it. The probability that he runs away screaming is 0.2 should he run away screaming his chance of getting caught and subsequently eaten by the wolf is 0.1. Should Ben foolishly decide to enter the house his probability of getting eaten is 0.9.

(A) Draw the tree diagram for this problem and label the probabilities appropriately.

(B) What is the probability that Ben survives this unfortunate situation?

(C) Given that Ben was eaten, what is the probability that he decided to enter the house?

Like I said, I was really happy with the way this activity turned out. It didn't take any more class time than usual and the kids had a blast writing, solving, and peer reviewing each others work. I need to do more of this.