Geometric probability deals with likelihood and chance. Traditionally, it attempts to find the odds of a certain outcome when using geometric objects. This works when dealing with games that involve geometric shapes. Many of the games you play and watch on television are simply problems involving geometric probability. By understanding probability, you can determine the odds of getting a certain score for these games.
In the game of dice, you attempt to get a specific number by rolling dice. This is a question about the odds of making one side of a cube show up on top. To determine the odds of winning a dice game with geometric probability, use the following equation:
Number of possible ways to roll a number/Number of sides
For example, when rolling a die, there is only one way to roll any number and there are six sides. The probability of rolling two is 1/6 or 0.167.
Wheel of Fortune
On the television show "Wheel of Fortune," players spin a large segmented wheel in an attempt to win a prize. Mathematically, they are playing the odds of landing on a certain sector. Determine the odds of landing on a certain sector with the following equation:
Total area of wheel / Area of one sector.
For a board with an area of 40 square inches divided into eight sectors, each with an area of 5 square inches, the probability of landing on any one sector is 5/40 = 1/8 or 0.125
Darts uses geometric probability much like Wheel of Fortune, but there are more sectors, and the area of each one differs. Participants play the odds of landing a dart into a specific section of the board. Use geometric probability to determine these odds with the equation:
Area of the section / Area of entire board
For example, the area of a dartboard is approximately 250 square inches. And the area of the double bulls eye is around 0.75 square inches. The probability of hitting the double bulls eye is 0.75/250 = 0.003.
The objective of Skeeball is to throw a wooden ball down a lane and land it in one of several holes. This is another game that involves geometric probability. To find the probability of landing the ball in any hole use the equation:
Area of hole/Area of board
For a Skeeball board with an area of 1,750 square inches, the probability of landing the ball in a hole with an area of 28 square inches is 28/1,750 = 7/432 = 0.016
Geometric probability allows you to determine the odds of scoring points in certain types games, but you can also factor in the skill level of the players. This requires knowledge of more complicated areas of probability and an understanding of mathematical modeling. To do this, you have to create a mathematical equation specific to the players and the game. Such equations use the skill level of each player and their statistics to create a type of handicap for less experienced players.