Q&A

# "A occurred" vs. "something must happen"

+0
−0
1. Why doesn't "Something must happen" mean $s_{actual} \in A$?

2. Scilicet, doesn't "A occurs" mean the same thing as "something must happen"? Something must happen. $\iff$ Some event must happen. $\iff$ At least one event must happen $\iff$ Call this event A. Then A occurred.

Blitzstein, Hwang. Introduction to Probability (2019 2 ed). p 6.

Why does this post require moderator attention?
Why should this post be closed?

+1
−0

$A$ is a specific event, specified beforehand.

Let's have an example. Let a random experiment be rolling a six-sided die and looking at what face lands up. The sample space is $S=\{1,2,3,4,5,6\}$.

What is event $A$? Let's specify it before the experiment is done. Let $A$ be the event that an even number lands up, that is, $A=\{2,4,6\}$.

Say the experiment is done and the outcome is $2$. Did $A$ occur? Since $2\in A$, the answer is yes.

Say the experiment is done again and there was an outcome $s$, but we don't know what it was. Can we say $s\in A$? No. Can we say $s\not\in A$? No. But we can say that something happened, that is, $s\in S$.

Why does this post require moderator attention?

Featured
Hot Posts

This community is part of the Codidact network. We have other communities too — take a look!

Want to advertise this community? Use our templates!

Like what we're doing? Support us!