Stats 3.2Concept6 parts

Conditional Probability and Independence

Update a probability given evidence, and tell independent events from mutually exclusive ones.

Loading your progress…Next: 3.3 Bayes' Theorem

In this lesson6 parts

  1. 01Keep the whole inbox in view
  2. 02Restrict to the messages that were flagged
  3. 03Reverse the condition without swapping the meaning
  4. 04Does knowing spam status change the flag rate?
  5. 05Exclusion asks a different question
  6. 06Reconstruct the counts in code

Key terms

The words this lesson introduces, each in one line. The module’s glossary collects them all.

conditional probability (narration)
A fraction calculated inside a restricted group: P(A given B) counts the outcomes in both and divides by all of B. P(spam given flagged) = 9 / 108.
given (narration)
The word that names the group used as the denominator.
independence
Knowing one event does not change the probability of the other.
mutually exclusive
Two events with no shared outcomes, such as spam and real.
feature (narration)
A recorded property of a message, such as whether a certain word appears in it.

Quiz 5 questions

Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.

Practice

Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.

The self-checking notebook for this lesson is Conditional probability, independence and Bayes' theorem.

Common mistakes

What you will see when it goes wrong, why it happens, and the fix.

Where it’s used

Where this lesson’s ideas turn up in real work.