Concetti Base della Probabilità
Comprendere concetti e principi fondamentali della probabilità
Interactive Basic Probability Concepts Visualization
Welcome to the Basic Probability Concepts Explorer
This interactive visualization helps you understand fundamental probability concepts including sample spaces, events, unions, intersections, complements, and probability calculations.
What you can explore:
- Sample Space - All possible outcomes of an experiment
- Events - Subsets of the sample space
- Union (A ∪ B) - Outcomes in A or B or both
- Intersection (A ∩ B) - Outcomes in both A and B
- Complement (A') - Outcomes not in A
- Probability - P(A) = favorable outcomes / total outcomes
How to Use This Visualization
Interactive Features:
- • Select Visualization Mode - Venn diagram, tree diagram, or experiment view
- • Choose Sample Space - Dice, coins, cards, or spinner
- • Toggle Highlights - Show union, intersection, or complement
- • View Calculations - See probability formulas and results
What You'll See:
- • Venn Diagram - Visual representation of events and their relationships
- • Tree Diagram - Sequential probability visualization
- • Experiment View - Sample space with colored outcomes
- • Probability Panel - Real-time probability calculations
Probability Calculations
P(Event A)
0.500
3 / 6 = 0.500
P(Event B)
0.500
3 / 6 = 0.500
P(A ∩ B)
0.167
1 / 6 = 0.167
P(A ∪ B)
0.833
5 / 6 = 0.833
P(A) + P(B) - P(A ∩ B) = 0.500 + 0.500 - 0.167 = 0.833
Key Concepts
Sample Space: The set of all possible outcomes. Denoted by S. Total outcomes: 6
Event: A subset of the sample space. P(Event) = favorable outcomes / total outcomes
Union (A ∪ B): Outcomes in A or B or both. P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Intersection (A ∩ B): Outcomes in both A and B. P(A ∩ B) = 0.167
Probability Rules
• 0 ≤ P(A) ≤ 1
• P(S) = 1
• P(A') = 1 - P(A)
• P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
• If A and B are mutually exclusive:
P(A ∪ B) = P(A) + P(B)
Lezioni
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