**Project Overview**

When we started the Playing with History project, we were introduced by a game called "The Game of Pig." In this game, 2 or more people receive two dice to share. Whoever reaches the sum of 50 first out of the players wins that round. This is a game of chance and that is because someone could either roll the die many times and risk losing, but getting lots of tallies or they could roll for a short number of times, and not risk getting so many points or losing. We were expected to learn probability and chances.

**Probability definition**

"The extent to which something is probable; the likelihood of something happening or being the case."

**Observed Probability**

"In **probability** and statistics, a realization, **observation**, or **observed** value, of a random variable is the value that is actually **observed** (what actually happened). The random variable itself is the process dictating how the **observation** comes about."

**Theoretical**

**Theoretical** **probability**: **probability** based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes. See also: **Probability**. Experimental **Probability**.

**Conditional**

"The probability of an event (**A**) given that another (**B**) has already occurred."

**Probability of Multiple Events**

To find the **probability** of two independent **events** that occur in sequence, find the **probability** of each **event** occurring separately, and then multiply the **probabilities**. This multiplication rule is **defined** symbolically below.

**Expected Value**

A predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

**Two-Way Tables**

A **two-way** **table** of counts organizes data about **two** categorical variables.

**Tree Diagram**

A thing that has a branching structure resembling that of a tree.

**Joint Probability**

A **joint** **probability** is a statistical measure where the likelihood of two events occurring together and at the same point in time are calculated. **Joint** **probability** is the **probability** of event Y occurring at the same time as event X occurs.

**Marginal Probability**

In **probability** theory and statistics, the **marginal** distribution of a subset of a collection of random variable is the **probability** of the variables contained in the subset.

**Renaissance Game**

The board game Fox and Geese was said to be created in 1697. The design on the board looks complex with squares, rectangles, and diagonal lines in the small squares. In this game, it requires two players. There are 33 points on the board to move the game piece(s) to. One player is the fox which could move in every direction of the board: forward, backwards, and side to side. The fox can also use any lines in the board which includes the diagonal lines that leads to the points. The other player receives 15, 17, or 18 game pieces which are the geese. The geese can only move forward, diagonally forward, and side to side. The geese can prevent the fox from being able to move and win if they surround the fox in all directions with more than one behind the other. This is because if there's one space behind the geese then the fox can jump across that geese and the other player loses that game piece. If the fox captures every goose on the board, then it wins. This is a game of inequality, so the players have to take chances to try to win.

**Project Overview**When we started the Playing with History project, we were introduced by a game called "The Game of Pig." In this game, 2 or more people receive two dice to share. Whoever reaches the sum of 50 first out of the players wins that round. This is a game of chance and that is because someone could either roll the die many times and risk losing, but getting lots of tallies or they could roll for a short number of times, and not risk getting so many points or losing. We were expected to learn probability and chances.

**Probability definition**

"The extent to which something is probable; the likelihood of something happening or being the case."

**Observed Probability**

"In

**probability**and statistics, a realization,

**observation**, or

**observed**value, of a random variable is the value that is actually

**observed**(what actually happened). The random variable itself is the process dictating how the

**observation**comes about."

**Theoretical**

**Theoretical**

**probability**:

**probability**based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes. See also:

**Probability**. Experimental

**Probability**.

**Conditional**

"The probability of an event (

**A**) given that another (

**B**) has already occurred."

**Probability of Multiple Events**

To find the

**probability**of two independent

**events**that occur in sequence, find the

**probability**of each

**event**occurring separately, and then multiply the

**probabilities**. This multiplication rule is

**defined**symbolically below.

**Expected Value**

A predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

**Two-Way Tables**

A

**two-way**

**table**of counts organizes data about

**two**categorical variables.

**Tree Diagram**

A thing that has a branching structure resembling that of a tree.

**Joint Probability**

A

**joint**

**probability**is a statistical measure where the likelihood of two events occurring together and at the same point in time are calculated.

**Joint**

**probability**is the

**probability**of event Y occurring at the same time as event X occurs.

**Marginal Probability**

In

**probability**theory and statistics, the

**marginal**distribution of a subset of a collection of random variable is the

**probability**of the variables contained in the subset.

**Renaissance Game**The board game Fox and Geese was said to be created in 1697. The design on the board looks complex with squares, rectangles, and diagonal lines in the small squares. In this game, it requires two players. There are 33 points on the board to move the game piece(s) to. One player is the fox which could move in every direction of the board: forward, backwards, and side to side. The fox can also use any lines in the board which includes the diagonal lines that leads to the points. The other player receives 15, 17, or 18 game pieces which are the geese. The geese can only move forward, diagonally forward, and side to side. The geese can prevent the fox from being able to move and win if they surround the fox in all directions with more than one behind the other. This is because if there's one space behind the geese then the fox can jump across that geese and the other player loses that game piece. If the fox captures every goose on the board, then it wins. This is a game of inequality, so the players have to take chances to try to win.