Home › BAF (Bachelor of Accounting & Finance) › Business Statistics › Probability Topics › What does conditioning on an event B do to the s…
What does conditioning on an event B do to the sample space?
AIt leaves the sample space completely unchanged
BIt doubles the sample space to allow for B
CIt reduces the sample space to the outcomes of B
DIt replaces the sample space with the union set
Answer & Solution
Correct answer: C. It reduces the sample space to the outcomes of B
1. Saying that B has already occurred rules out every outcome outside B.
2. The sample space therefore shrinks to the outcomes of B alone.
3. The probability of A is then measured against that reduced space rather than against the original one.
4. Leaving the sample space unchanged would make the conditional identical to the plain probability, which only happens when the events are independent.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.1 Terminology_
Related questions
An experiment whose result is not predetermined is called a:A conditional probability differs from an ordinary one because the count is divided by:On a fair six-sided die, the outcome of any one face is:A sample space can be represented by listing outcomes, by a Venn diagram, or by a:Sampling without replacement makes successive picks dependent because:Sampling with replacement means each member picked:Two events are independent when the outcome of the first:Independent and mutually exclusive are terms that: