exercise:Ac24f1d3f1: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> <ul><li> For events <math>A_1</math>, \dots, <math>A_n</math>, prove that <math display="block"> P(A_1 \cup \cdots \cup A_n) \leq P(A_1) + \cdots + P(A_n)\ . </math> </li> <li> For events <math>A</math> and <math>B</math>, prove that <math disp...") |
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<ul><li> For events <math>A_1 | <ul style="list-style-type:lower-alpha"> | ||
<li> For events <math>A_1, \dots, A_n</math>, prove that | |||
<math display="block"> | <math display="block"> | ||
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</math> | </math> | ||
</li> | </li> | ||
<li> For events <math>A</math> and <math>B</math>, prove that | <li> | ||
For events <math>A</math> and <math>B</math>, prove that | |||
<math display="block"> | <math display="block"> | ||
P(A \cap B) \geq P(A) + P(B) - 1. | P(A \cap B) \geq P(A) + P(B) - 1. | ||
Latest revision as of 00:21, 14 June 2024
[math]
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}[/math]
- For events [math]A_1, \dots, A_n[/math], prove that
[[math]] P(A_1 \cup \cdots \cup A_n) \leq P(A_1) + \cdots + P(A_n)\ . [[/math]]
-
For events [math]A[/math] and [math]B[/math], prove that
[[math]] P(A \cap B) \geq P(A) + P(B) - 1. [[/math]]