Expected Value: Day 1

Today should be somewhat of a review of permutations and combinatorics. Some sample problems include:

1. What is the probability of flipping a coin 5 times and getting 5 heads?

2. What is the probability that out of four coin flips, two will be heads?

3. What is the probability of rolling a 5, a 6, and a 2 (in that order)?

4. What is the probability of rolling a 5, a 6, and a 2 (in any order)?

5. Out of four draws from a deck of cards (with replacement), what is the probability of drawing four hearts?

6. Out of four draws form a deck of cards (without replacement), what is the probability of drawing four hearts?

Begin to introduce the concept of modeling by having the students do these experiments with actual coins, dice, and cards. Also give the students some very simple modeling problems such as:

1. The Martinez family has three children.
   • What is the probability that the children are all boys?
   • What is the probability that the children are all girls?
   • What is the probability that there are two boys and only one girl?

2. There are twenty children born in a hospital on Christmas Day.
   • What is the chance that all are girls?
   • What is the chance that exactly 10 are boys?
   • What is the chance that only 5 are girls?

Make sure the students get to solve these problems both analytically and empirically as they build their sense of how the two relate to one another.

If you like, you may return to the introduction page.

Go on to the lesson plan for Day 2