# MATHEMATICS

**How many kids signed up for “Little Tykes” under the age of seven?**

**(1 pt)**

**?**

(Select a multiple of 10, of at least 20)

**How many kids signed up for “Big Kids” between 8 and 12?**

**(1 pt)**

**?**

(Select a multiple of 10, of at least 20)

**How many kids signed up for “Teens” between 13 and 18?**

**(1 pt)**

**?**

(Select a multiple of 10, of at least 20)

**How many different ways can you create teams of ten for the “Little Tykes” grade level?**

**(2 pts)**

**?**

**Show your work: (2 pts)**

**If age levels did not matter, how many different ways can you create teams of ten?**

**(2 pts)**

**?**

**Show your work: ** **(2 pts)**

**Part B: Probabilities and Odds**

**4.** For this set of exercises, you will need one standard six sided dice. If you don’t have one, you can use virtual dice: https://www.random.org/dice/, (**40 points total)**

**a.** First, let’s differentiate between “odds” and “probability”.

**How are odds and probability different?**

**(2 pts)**

**?**

**What is the “odds of in favor” ratio?**

**(3 pts)**

**?**

**What is the “probability of an event” ratio?**

** (3 pts)**

**?**

**What are the odds of rolling a three? (Simplify all fraction answers.)**

** (2 pts)**

**?**

**What is the theoretical probability of rolling a three? (Simplify all fraction answers.)**

** (2 pts)**

**?**

**b.** Please reflect on the previous question’s answer outcome. First, convert the fraction to a percent.

**Percent Probability**

**Theoretical Probability (Rounded to the nearest whole percent.)**

**(2 pts)**

**?**

Next, given the “Likelihood Scale” table above, what term best describes your answer?

**Likelihood Scale**

**Term**

**(2 pts)**

**?**

**a.** What if someone challenged you to **NEVER** roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of **never** getting a three?

**Percent Probability**

**Solution:**

**(Rounded to the nearest whole percent.)**

**(2 pts)**

**?**

**Show your work:** **(2 pts)**

**b.** After 18 rolls, what would be the empirical probability of getting a three on at least one of those rolls? Also, list the “Likelihood Scale” term from the table above.

**Percent Probability**

**Empirical Probability **

**(Rounded to the nearest whole percent.)**

**(2 pts)**

**?**

**Likelihood Scale Term**

**(2 pts)**

**?**

**c.** What if someone challenged you to **NEVER** roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of **never** getting a three?

**Percent Probability**

**Solution:**

**(Rounded to the nearest whole percent.)**

**(2 pts)**

**?**

**Show your work: ** **(2 pts)**

**What do you notice about the answers for parts c. and d. above?**

**(2 pts)**

**?**

**d.** Roll the dice 18 times and keep track of what is rolled in the table below.** (2 points)**

**Roll #**

**Dice**

**Roll #**

**Dice**

**Roll #**

**Dice**

Roll 1

**?**

Roll 7

**?**

Roll 13

**?**

Roll 2

**?**

Roll 8

**?**

Roll 14

**?**

Roll 3

**?**

Roll 9

**?**

Roll 15

**?**

Roll 4

**?**

Roll 10

**?**

Roll 16

**?**

Roll 5

**?**

Roll 11

**?**

Roll 17

**?**

Roll 6

**?**

Roll 12

**?**

Roll 18

**?**