Matematické Fórum

stuart clark · 11. 04. 2016 04:38

There is a line of length $a$ unit (where $a$ is fixed positive real number), The point $P$ and $Q$ choosen randomly

(uniformly) on this line, Let $b$ be a fixed real number satisfying $0\leq b \leq a\;,$ Then probability that $PQ>b$

vanok · 12. 04. 2016 00:52 — Editoval vanok (12. 04. 2016 08:41)

Hi ↑ stuart clark:,
Let us choose the coordinates of P, Q x and y respectively. So $PQ > b$ expresses as $|x-y | > b$ and so I(x,y) bas to be in 2 regions of squared ABCD of coordinates (0,0), (a , 0), (a , a), (0, a) in an orthonormal Cartesian coordinate system, containing vertices B and D and bounded by two straight lignes of equations $x-y=b$ and $-x+y=b$ . (Make the figure)
So your probability is $\frac {(a-b)^2}{a^2}$

stuart clark · 16. 04. 2016 04:49

Thanks ↑ vanok:.

Matematické Fórum

#1 11. 04. 2016 04:38

Probability

#2 12. 04. 2016 00:52 — Editoval vanok (12. 04. 2016 08:41)

Re: Probability

#3 16. 04. 2016 04:49

Re: Probability

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