A-point-A-is-randomly-chosen-in-a-square-of-side-length-1-unit-Find-the-probability-the-distance-from-A-to-the-centre-of-the-square-does-not-exceed-x-

Question Number 18945 by Tinkutara last updated on 01/Aug/17

A point^{'} A^{'} is randomly chosen in a

square of side length 1 unit . Find the

probability the distance from A to the

centre of the square does not exceed x .

Commented by dioph last updated on 02/Aug/17

Area of square S : A_{S} = 1

Area of circle C with radius x : A_{C} = π x^{2}

say point is P :

p (P \in C ∣ P \in S) = \frac{p (P \in C \cap S)}{p (P \in S)}

= {\begin{cases} \frac{A_{C}}{A_{S}} = π x^{2}, if x ⩽ 0.5 \\ \frac{A_{C \cap S}}{A_{S}} = \dots, if 0.5 < x ⩽ \frac{\sqrt{2}}{2} \\ \frac{A_{S}}{A_{S}} = 1, if x > \frac{\sqrt{2}}{2} \end{cases}

working on second case

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