# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

[Search all questions & derivations →](/en/explore/)

1 1 results · Page 1 of 1



Concept guide



## [Probability on finite sample spaces: validating a weight model, computing event probabilities and complements](/en/derivations/derivation-mko-probability-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-probability)

Let S={1,2,3,4} with the full powerset as event family and weights w_1=1/2, w_2=1/3, w_3=1/6, w_4=0. Verify that this is a legal finite probability model; prove from the definition the identities P(∅)=0 and P(S)=1, additivity for disjoint events, and the complement identity P(S∖E)=1−P(E); compute P({1,3}) and explain why it differs from |E|/|S|; show that {4} is nonempty yet has probability 0; and decide that the candidate weights (1/2,1/3,1/3,0) and (1/2,2/3,−1/6,0) are both illegal.

Probability on finite sample spaces

derivation-mko-probability-01





1 1 results · Page 1 of 1