12 Questions
ما هو تعريف الاحتمال؟
قياس احتمال حدوث حدث ما
ما هو.setName() للاحداث المستقلة؟
حوادث مستقلة
ما هو قاعدة الجمع لاحتمال حدوث حدثين؟
مجموع احتمالات الحدثين ناقص احتمال تلاقيهم
ما هو 名称 للاحداث التي تشمل جميع النتائج الممكنة؟
أحداث شاملة
ما هو القانون لاحتمال حدوث حدثين مستقلين؟
積 احتمالات الحدثين
ما هو الاسم لصيغة تحديث الاحتمال لحدث ما بعد حدوث حدث آخر؟
مبدأ بايز
ما هو الفرق بين الاحتمال النظري والاحتمال التجريبي؟
الاحتمال النظري يعتمد على عدد النتائج الممكنة بينما الاحتمال التجريبي يعتمد على نتائج التجارب المتكررة
ما هو规則 الجمع لاحتمال حدوث حدثين متداخلين؟
P(E ∪ F) = P(E) + P(F) - P(E ∩ F)
ما هو الاسم لصيغة تحديث الاحتمال لحدث ما بعد حدوث حدث آخر؟
الاحتمال الشرطي
ما هو النوع من الاحتمال الذي يعتمد على الحكم الشخصي؟
الاحتمال الشديد
ما هو规ếu لاحتمال حدوث حدث ما في المجال الاحتمالي؟
P(E) ≤ 1
ما هو الفرق بين الحدث والحدث المستقل؟
الحدث هو مجال الاحتمال بينما الحدث المستقل هو نتيجة أحداث متعددة
Study Notes
Basic Concepts
- Experiment: An action or situation that can produce a set of outcomes.
- Sample Space: The set of all possible outcomes of an experiment.
- Event: A subset of the sample space.
Probability Definition
- Probability: A measure of the likelihood of an event occurring.
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Probability Axioms:
- The probability of an event is a non-negative real number.
- The probability of the sample space is 1.
- The probability of the union of disjoint events is the sum of their individual probabilities.
Types of Events
- Independent Events: The occurrence of one event does not affect the probability of the other event.
- Dependent Events: The occurrence of one event affects the probability of the other event.
- Mutually Exclusive Events: The occurrence of one event implies the non-occurrence of the other event.
- Exhaustive Events: The events include all possible outcomes of the sample space.
Probability Rules
- Addition Rule: The probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.
- Multiplication Rule: The probability of the intersection of two independent events is the product of their individual probabilities.
Conditional Probability
- Conditional Probability: The probability of an event occurring given that another event has occurred.
- Bayes' Theorem: A formula for updating the probability of an event based on new information.
Random Variables
- Discrete Random Variable: A random variable that can only take on specific, distinct values.
- Continuous Random Variable: A random variable that can take on any value within a certain range or interval.
Probability Distributions
- Bernoulli Distribution: A discrete distribution for binary outcomes (success or failure).
- Binomial Distribution: A discrete distribution for the number of successes in a fixed number of independent trials.
- Uniform Distribution: A continuous distribution where every possible value has an equal probability.
- Normal Distribution: A continuous distribution that is symmetric and bell-shaped.
Test your understanding of probability concepts, including experiments, events, probability definition, types of events, probability rules, conditional probability, random variables, and probability distributions.
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