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دوره‌ها ماژول‌ها مجموعه‌داده‌ها منابع مدرس

آزمایشگاه داده‌های رسمی

منابع داده عمومی برای مثال‌ها، نمودارها و تمرین‌های R

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درس 5 از 16

Conditional Probability

خانه/ماژول‌ها/ماژول 5/Conditional Probability

Restrict the sample space to a named condition and calculate with the correct denominator.

دریافت PDF درس

40 دقیقه31% مسیر

هدف‌های یادگیریتا پایان این درس، دانشجویان می‌توانند:

1Define the events and probability quantities used in conditional probability.
2Select and calculate an appropriate probability rule with a visible denominator or assumption.
3Interpret the result for a business decision without overstating certainty or causation.

Theory

Core probability reasoning

Restrict the sample space to a named condition and calculate with the correct denominator.

توضیح 1

Condition: The event after given that defines the relevant group.

توضیح 2

Numerator: Cases satisfying both the target and condition.

توضیح 3

Denominator: All cases satisfying the condition.

اصطلاحات

Concept map

Condition

The event after given that defines the relevant group.

Given loyalty membership.

Numerator

Cases satisfying both the target and condition.

Digital receipt and loyalty.

Denominator

All cases satisfying the condition.

All loyalty members.

نمادگذاری و فرمول‌ها

Conditional probability

رابطه اصلی

P(A given B) = P(A and B) / P(B), P(B) > 0

Define every event before substituting values, then validate the result and denominator.

گام 1Name B.
گام 2Count or calculate A and B.
گام 3Divide by B and label the denominator.

فعالیت تعاملی

conditional probability lab

A and B casesB cases (denominator)

P(A given B)

0.15

18 / 120

The denominator is highlighted as all B cases because B is the event after given.

مثال حل‌شده

Digital receipts

سناریو

A retailer asks what share of loyalty members choose digital receipts.

Reversing A and B changes the question and usually the answer.

ارتباط با R

R note: Conditional and Joint Probability

Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.

Live R Lab

Conditional and Joint Probability

Calculate marginal, joint, conditional, and sequential probabilities with explicit denominators.

Editable R code

Results

Ready to run

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Name the conditioning event.

Validate the denominator.

Connect conditional and joint probability.

Dataset provenance

Original synthetic data generated for STATLAB Academy. No textbook data used.

Interpretation safeguard

Always name the conditioning event and its denominator.

بازاندیشی

مکث و یادداشت

Where could an unclear event definition or assumption change the conclusion in conditional probability?

Name the event, denominator, probability interpretation, and one operational limitation.

دستیار

Ask your probability coach

Help me reason through Conditional Probability by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.

ارزیابی پایانی

Lesson checkpoint

Use a hint before submitting if needed. Full calculations and interpretations appear after submission.

Checkpoint

Module 5 Lesson 5 Checkpoint

Question 1 of 2. Answered 0/2. Passing score: 70%.

برای دریافت بازخورد امتیازدهی‌شده و ذخیره پیشرفت، وارد شوید.ورود ساخت حساب

Question 1: Choose one

easyCalculate and responsibly interpret probability for a defined event.

In P(Return given Express), which cases form the denominator?

Express ordersAll ordersNon-express ordersReturned orders

منبع

Recommended reading

Explore additional probability explanations and exercises from properly licensed or publisher resources.

منبع

Module 5 learning material

Download an original worksheet or guide for this lesson.

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