exercise:2aa4fcb3db: 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> Pick a point <math>x</math> at random (with uniform density) in the interval <math>[0,1]</math>. Find the probability that <math>x > 1/2</math>, given that <ul><li> <math>x > 1/4</math>. </li> <li> <math>x < 3/4</math>. </li> <li> <math>|x...") |
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Pick a point <math>x</math> at random (with uniform density) in the interval | |||
<math>[0,1]</math>. Find the probability that <math>x > 1/2</math>, given that | <math>[0,1]</math>. Find the probability that <math>x > 1/2</math>, given that | ||
<ul><li> <math>x > 1/4</math>. | <ul style="list-style-type:lower-alpha"><li> <math>x > 1/4</math>. | ||
</li> | </li> | ||
<li> <math>x < 3/4</math>. | <li> <math>x < 3/4</math>. | ||
Latest revision as of 00:24, 14 June 2024
Pick a point [math]x[/math] at random (with uniform density) in the interval [math][0,1][/math]. Find the probability that [math]x \gt 1/2[/math], given that
- [math]x \gt 1/4[/math].
- [math]x \lt 3/4[/math].
- [math]|x - 1/2| \lt 1/4[/math].
- [math]x^2 - x + 2/9 \lt 0[/math].