Unit 12 probability homework 3 geometric probability answer key – Welcome to Unit 12 Probability Homework 3: Geometric Probability Answer Key. This comprehensive guide provides a thorough understanding of geometric probability, equipping you with the knowledge and skills to solve complex problems in various fields. Dive into the fascinating world of geometric probability and uncover its practical applications in real-world scenarios.
Geometric Probability
Geometric probability is a branch of mathematics that deals with the probability of events that occur in a geometric setting. It is used to calculate the likelihood of events that occur in a specific geometric shape or pattern.
Geometric probability problems often involve calculating the area or volume of a region, or the length of a curve. These problems can be solved using a variety of techniques, including integration, calculus, and trigonometry.
Geometric Probability Formula
The formula for geometric probability is:
P(E) = A / T
where:
- P(E) is the probability of the event
- A is the area of the region where the event can occur
- T is the total area of the geometric shape
Applications of Geometric Probability
Geometric probability has a wide range of applications in various fields, including:
- Architecture
- Engineering
- Physics
- Computer science
For example, geometric probability is used to calculate the probability of a projectile hitting a target, the probability of a molecule colliding with another molecule, and the probability of a computer program running successfully.
Geometric Probability Examples
| Problem | Solution | Explanation |
|---|---|---|
| What is the probability of a dart hitting a circular target with a radius of 10 cm? The dart is thrown from a distance of 50 cm from the center of the target. | 0.25 | The area of the circular target is πr² = π(10)² = 100π cm². The area of the region where the dart can hit is the area of the circle with radius 50 cm, which is π(50)² = 2500π cm². Therefore, the probability of hitting the target is 100π / 2500π = 0.25. |
| What is the probability of a ball landing in a rectangular box with a length of 10 cm, a width of 5 cm, and a height of 3 cm? The ball is dropped from a height of 10 cm above the box. | 0.6 | The volume of the rectangular box is 10 cm × 5 cm × 3 cm = 150 cm³. The volume of the region where the ball can land is the volume of the box, which is 150 cm³. Therefore, the probability of landing in the box is 150 cm³ / 150 cm³ = 0.6. |
Geometric Probability Exercises, Unit 12 probability homework 3 geometric probability answer key
- A dart is thrown at a circular target with a radius of 5 cm. The dart is thrown from a distance of 10 cm from the center of the target. What is the probability of hitting the target?
- A ball is dropped from a height of 10 cm above a rectangular box with a length of 10 cm, a width of 5 cm, and a height of 3 cm. What is the probability of the ball landing in the box?
- A coin is flipped three times. What is the probability of getting at least one head?
Answer Key
- 0.25
- 0.6
- 0.875
Top FAQs: Unit 12 Probability Homework 3 Geometric Probability Answer Key
What is geometric probability?
Geometric probability deals with the likelihood of an event occurring within a specific geometric region or shape.
How is geometric probability calculated?
Geometric probability is calculated using the formula P(X = k) = (1 – p)^(k-1) – p, where k represents the number of trials, p represents the probability of success on each trial, and X represents the random variable.
What are some real-world applications of geometric probability?
Geometric probability finds applications in fields such as engineering, physics, computer science, and quality control.
