exercise:6b8656ac6e: 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> Take a stick of unit length and break it into three pieces, choosing the break points at random. (The break points are assumed to be chosen simultaneously.) What is the probability that the three pieces can be used to form a triangle? '' Hint'...") |
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\newcommand{\mathds}{\mathbb}</math></div> Take a stick of unit length and break it into | \newcommand{\mathds}{\mathbb}</math></div> Take a stick of unit length and break it into three pieces, choosing the break points at random. (The break points are assumed to be chosen simultaneously.) What is the probability that the three pieces can be used to form a triangle? | ||
three pieces, choosing the break points at random. (The break points are assumed | |||
to be chosen simultaneously.) What is the probability that the three pieces | '' Hint'': The sum of the lengths of any two pieces must exceed the length of the third, so each piece must have length <math> < 1/2</math>. Now use [[exercise:246cabd63e |Exercise(g)]]. | ||
can be used to form a triangle? '' Hint'': | |||
The sum of the lengths of any two pieces must exceed the length | |||
of the third, so each piece must have length <math> < 1/2</math>. Now use | |||
Latest revision as of 23:23, 12 June 2024
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Take a stick of unit length and break it into three pieces, choosing the break points at random. (The break points are assumed to be chosen simultaneously.) What is the probability that the three pieces can be used to form a triangle?
Hint: The sum of the lengths of any two pieces must exceed the length of the third, so each piece must have length [math] \lt 1/2[/math]. Now use Exercise(g).