Conditional probability and independence
Probability of A given B, reading it in a two-way table and in a weighted tree, the product rule, the independence test, and the difference between mutually exclusive and independent events.
- 28 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
- Understand
A few cards from the deck
Conditional probability: what is it?
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The probability of A when B is known to have happened, written P(A | B) and equal to P(A ∩ B) / P(B), with P(B) non-zero.
The information “B happened” shrinks the sample space to B. P(A | B) and P(B | A) are two different numbers: the probability of being slow given a cache miss is not that of a cache miss given slow.
500 logins: 300 from a phone of which 60 fail, 200 from a computer of which 20 fail. What is P(failure | phone)?
20%12%75%30%
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20%We work inside the “phone” subgroup: 60 failures out of 300. 12% (60/500) divides by the grand total, 75% (60/80) reverses the conditioning and gives P(phone | failure), 30% (60/200) divides by the other row's total.
P(A | B) is computed by dividing P(A ∩ B) by …, provided P(B) is ….
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P(A | B) is computed by dividing P(A ∩ B) by P(B), provided P(B) is non-zero.
We divide by the probability of what we know, not of what we look for: B becomes the new sample space.
Independent events: what is it?
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Two events such that one happening does not change the probability of the other: P(A ∩ B) = P(A) × P(B).
Checked by calculation, not by intuition. If P(A | B) = P(A), then P(A ∩ B) = P(B) × P(A | B) = P(A) × P(B).