There-are-two-cards-one-is-yellow-on-both-sides-and-the-other-one-is-yellow-in-one-side-and-red-on-the-other-The-cards-have-the-same-probability-1-2-of-being-chosen-and-one-is-chosen-and-placed

Question Number 111826 by Aina Samuel Temidayo last updated on 05/Sep/20

$$\mathrm{There}\:\mathrm{are}\:\mathrm{two}\:\mathrm{cards};\:\mathrm{one}\:\mathrm{is}\:\mathrm{yellow}\:\mathrm{on} \\ $$$$\mathrm{both}\:\mathrm{sides}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{one}\:\mathrm{is}\:\mathrm{yellow} \\ $$$$\mathrm{in}\:\mathrm{one}\:\mathrm{side}\:\mathrm{and}\:\mathrm{red}\:\mathrm{on}\:\mathrm{the}\:\mathrm{other}.\:\mathrm{The} \\ $$$$\mathrm{cards}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{probability}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\mathrm{of}\:\mathrm{being}\:\mathrm{chosen},\:\mathrm{and}\:\mathrm{one}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{and} \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{the}\:\mathrm{table}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{upper}\:\mathrm{side} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{card}\:\mathrm{on}\:\mathrm{the}\:\mathrm{table}\:\mathrm{is}\:\mathrm{yellow}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{under} \\ $$$$\mathrm{side}\:\mathrm{is}\:\mathrm{also}\:\mathrm{yellow}\:\mathrm{is}. \\ $$

Commented by Her_Majesty last updated on 05/Sep/20

$${case}\:\mathrm{1}\:\frac{{r}}{{y}}\:\left({doesn}'{t}\:{count}\right) \\ $$$${case}\:\mathrm{2}\:\frac{{y}}{{r}} \\ $$$${case}\:\mathrm{3}+\mathrm{4}\:\frac{{y}}{{y}} \\ $$$$\Rightarrow\:{probability}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Commented by Aina Samuel Temidayo last updated on 05/Sep/20

$$\mathrm{Ok}. \\ $$

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