## Sunday, March 6, 2011

Here are the directions for the Probability exercises that we did.

Probability I
When you toss a coin, how many possible outcomes are there?
How many outcomes can there be at one time? In other words, can I toss a coin and get both heads and tails?
We say that the probability that something will happen is the number of ways to get that outcome out of the total number of outcomes.
For a coin toss, there is a 1 out of 2 chances that I will get heads. This means 1/2 or half the time. Toss a quarter ten times and keep track of the number of times you get heads.

(For Probability activities II and III, a "sock drawer" was created using a small basket and a number of pairs of baby socks. The socks in the basket were as follows: two blue socks, four pink socks, six white socks.)

Probability II
Remember that the probability of an event is the number of ways to get that outcome over the total number of outcomes.
Look through the sock drawer.
If you close your eyes and pull out a sock at random, what are the chances you will get a pink sock? A white sock?

Probability III
Probability gives us an idea about our chances, but sometimes we really need to be sure! After all, who wants to walk around wearing socks that don't match?
Suppose you wake up and it is dark because the power has gone out. You will have to grab some socks and bring them with you to school -- hopefully you will have a match! You have six white socks, four pink socks, and two blue socks in the drawer.
How many socks will you need to take to guarantee you will have a matching pair of socks (any color)?
How many socks will you need to take to guarantee you have a matching pair of white socks?

(The mathematician pointed out that the skill students are learning here is the value of negation. When they need to determine the number of socks required to guarantee a pair of white socks, this means the need to determine the number of socks that are not white -- as in, worst case scenario, they have grabbed all those first -- plus the two white socks. To be 100% sure you have something you need means you need to have everything you don't need also!)  