exercise:9115005d87: 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> A point <math>P</math> in the unit square has coordinates <math>X</math> and <math>Y</math> chosen at random in the interval <math>[0,1]</math>. Let <math>D</math> be the distance from <math>P</math> to the nearest edge of the square, and <math>E...") |
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A point <math>P</math> in the unit square has coordinates <math>X</math> and | |||
<math>Y</math> chosen at random in the interval <math>[0,1]</math>. Let <math>D</math> be the distance from | <math>Y</math> chosen at random in the interval <math>[0,1]</math>. Let <math>D</math> be the distance from | ||
<math>P</math> to the nearest edge of the square, and <math>E</math> the distance to the nearest corner. | <math>P</math> to the nearest edge of the square, and <math>E</math> the distance to the nearest corner. | ||
What is the probability that | What is the probability that | ||
<ul><li> <math>D < 1/4</math>? | <ul style="list-style-type:lower-alpha"><li> <math>D < 1/4</math>? | ||
</li> | </li> | ||
<li> <math>E < 1/4</math>? | <li> <math>E < 1/4</math>? | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 02:03, 14 June 2024
A point [math]P[/math] in the unit square has coordinates [math]X[/math] and [math]Y[/math] chosen at random in the interval [math][0,1][/math]. Let [math]D[/math] be the distance from [math]P[/math] to the nearest edge of the square, and [math]E[/math] the distance to the nearest corner. What is the probability that
- [math]D \lt 1/4[/math]?
- [math]E \lt 1/4[/math]?