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Question Number 10117 by Gaurav3651 last updated on 25/Jan/17
A point is chosen at random inside  a rectangle measuring 5 inches  by 6 inches.What is the probability  that the randomly selected point  is at least 1 inch from the edge of  rectangle?
$${A}\:{point}\:{is}\:{chosen}\:{at}\:{random}\:{inside} \\ $$$${a}\:{rectangle}\:{measuring}\:\mathrm{5}\:{inches} \\ $$$${by}\:\mathrm{6}\:{inches}.{What}\:{is}\:{the}\:{probability} \\ $$$${that}\:{the}\:{randomly}\:{selected}\:{point} \\ $$$${is}\:{at}\:{least}\:\mathrm{1}\:{inch}\:{from}\:{the}\:{edge}\:{of} \\ $$$${rectangle}? \\ $$
Commented by prakash jain last updated on 25/Jan/17
Favorable case is when the point  lies inside inner rectangle of 3×4.  Total cases: any point in 5×6 rectangle.
$$\mathrm{Favorable}\:\mathrm{case}\:\mathrm{is}\:\mathrm{when}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{lies}\:\mathrm{inside}\:\mathrm{inner}\:\mathrm{rectangle}\:\mathrm{of}\:\mathrm{3}×\mathrm{4}. \\ $$$$\mathrm{Total}\:\mathrm{cases}:\:\mathrm{any}\:\mathrm{point}\:\mathrm{in}\:\mathrm{5}×\mathrm{6}\:\mathrm{rectangle}. \\ $$

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