Question-170584

Question Number 170584 by Shrinava last updated on 27/May/22

Commented by mr W last updated on 27/May/22

$${i}\:{don}'{t}\:{think}\:{you}\:{mean} \\ $$$$\left[{AMSQ}\right]\:\vee\:\left[{NSPC}\right]. \\ $$

Commented by Shrinava last updated on 27/May/22

$$\mathrm{Sorry}\:\mathrm{dear}\:\mathrm{professor}\:\mathrm{yes} \\ $$

Commented by mr W last updated on 27/May/22

$${S}\:{lies}\:{always}\:{in}\:\left[{AMSQ}\right]\:\vee\:\left[{NSPC}\right]! \\ $$$${please}\:{check}\:{the}\:{question}\:{again}! \\ $$

Commented by Shrinava last updated on 27/May/22

$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$\mathrm{can}\:\mathrm{by}\:\mathrm{in}\:\mathrm{DQSP}\:\mathrm{or}\:\mathrm{PSNC}\:\mathrm{not}\:\mathrm{only}\:\mathrm{in} \\ $$$$\mathrm{AMSQ}\:\mathrm{or}\:\mathrm{NSPC}, \\ $$$$\mathrm{or}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\mathrm{MBNS}, \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\mathrm{4}\:\mathrm{quadrilaterals} \\ $$

Commented by mr W last updated on 27/May/22

Commented by mr W last updated on 27/May/22

$${you}\:{can}\:{ask}\:{for}\:{the}\:{probability}\:{that}\:{S} \\ $$$${lies}\:{in}\:\left[{AMTQ}\right]. \\ $$

Commented by mr W last updated on 27/May/22

Commented by mr W last updated on 27/May/22

$${you}\:{can}\:{not}\:{ask}\:{for}\:{the}\:{probability} \\ $$$${that}\:{S}\:{lies}\:{in}\:\left[{ABSQ}\right].\:{because}\:{it}'{s} \\ $$$${always}\:\mathrm{100\%}.\:{since}\:{S}\:{lies}\:{always}\:{in} \\ $$$$\left[{AMSQ}\right]. \\ $$

Commented by Shrinava last updated on 27/May/22

$$\mathrm{If}\:\:\mathrm{S}\in\mathrm{Int}\left[\mathrm{ABCD}\right]-\mathrm{rectangle}\:,\:\mathrm{S}-\mathrm{fixed} \\ $$$$\mathrm{M}\in\left(\mathrm{AB}\right)\:,\:\mathrm{N}\in\left(\mathrm{BC}\right)\:,\:\mathrm{P}\in\left(\mathrm{CD}\right)\:, \\ $$$$\mathrm{Q}\in\left(\mathrm{DA}\right)\:,\:\mathrm{AM}=\mathrm{PC}\:,\:\mathrm{BN}=\mathrm{DQ} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a} \\ $$$$\mathrm{random}\:\mathrm{point}\:\mathrm{from}\:\:\mathrm{Int}\left[\mathrm{ABCD}\right] \\ $$$$\mathrm{lies}\:\mathrm{in}:\:\:\left[\mathrm{AMSQ}\right]\:\cup\:\left[\mathrm{NSPC}\right] \\ $$

Commented by Shrinava last updated on 27/May/22

$$\mathrm{Dear}\:\mathrm{professor}\:\mathrm{sorry}\:\mathrm{was}\:\mathrm{corrected} \\ $$

Commented by mr W last updated on 27/May/22

Commented by mr W last updated on 27/May/22

Commented by mr W last updated on 27/May/22

$${no}\:{certain}\:{solution}! \\ $$

Commented by Shrinava last updated on 27/May/22

$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$\mathrm{so}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{mistake}\:\mathrm{again}? \\ $$

Commented by mr W last updated on 27/May/22

$${yes}. \\ $$$${the}\:{hatched}\:{area}\:{is}\:{not}\:{defined}. \\ $$

Commented by Shrinava last updated on 27/May/22

$$\mathrm{Dera}\:\mathrm{professor}, \\ $$$$\mathrm{exactly}\:\mathrm{how}\:\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{given},\:\mathrm{please} \\ $$

Commented by mr W last updated on 28/May/22

$${for}\:{example}: \\ $$$${AM}={PC}=\frac{{AB}}{\mathrm{3}},\:{BN}={DQ}=\frac{{BC}}{\mathrm{2}} \\ $$

Commented by Shrinava last updated on 28/May/22

$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$\mathrm{if}\:\mathrm{possible}\:\mathrm{you}\:\mathrm{would}\:\mathrm{share}\:\mathrm{your} \\ $$$$\mathrm{wonderful}\:\mathrm{solution} \\ $$

Commented by mr W last updated on 28/May/22

$${p}=\frac{\left[{AMSQ}\right]+\left[{NSPC}\right]}{\left[{ABCD}\right]} \\ $$$$=\frac{\left[{ABQ}\right]+\left[{BPC}\right]}{\left[{ABCD}\right]} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$=\frac{\mathrm{5}}{\mathrm{12}} \\ $$

Commented by Shrinava last updated on 28/May/22

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much}\:\mathrm{dear}\:\mathrm{professor} \\ $$

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