Question Number 142489 by jlewis last updated on 01/Jun/21
$$\mathrm{In}\:\:\mathrm{a}\:\mathrm{certain}\:\mathrm{urn}\:\mathrm{there}\:\mathrm{are}\:\mathrm{3}\:\mathrm{blue}, \\ $$$$\mathrm{2red}\:\mathrm{and}\:\mathrm{5}\:\mathrm{yellow}\:\mathrm{marbles}. \\ $$$$\mathrm{Calculate}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{atmost} \\ $$$$\mathrm{2}\:\mathrm{marbles}\:\mathrm{will}\:\mathrm{be}\:\mathrm{red}\:\mathrm{if}\:\mathrm{3}\:\mathrm{marbles} \\ $$$$\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{without}\:\mathrm{replacement} \\ $$
Commented by mr W last updated on 01/Jun/21
$${at}\:{most}\:\mathrm{2}\:{red}\:{marbles}\:{means}: \\ $$$${no}\:{red}\:{marble}\:{or} \\ $$$${one}\:{red}\:{marble}\:{or} \\ $$$${two}\:{red}\:{marbles}. \\ $$$${that}\:{means}\:{all}\:{possibilities}! \\ $$$$\Rightarrow{p}=\mathrm{1} \\ $$
Commented by jlewis last updated on 02/Jun/21
$$\mathrm{please}\:\mathrm{help},\mathrm{how}\:\mathrm{does}\:\mathrm{that} \\ $$$$\:\mathrm{comes}\:\mathrm{to}\:\mathrm{be} \\ $$
Commented by mr W last updated on 02/Jun/21
$${when}\:{you}\:{take}\:{three}\:{marbles}\:{from}\:{the} \\ $$$${urn},\:{there}\:{are}\:{only}\:{following}\:{cases}: \\ $$$${no}\:{red}\:{marble} \\ $$$${one}\:{red}\:{marble} \\ $$$${two}\:{red}\:{marbles} \\ $$$${so}\:{the}\:{probabilty}\:{that}\:{at}\:{most}\:{two} \\ $$$${red}\:{marbles}\:{are}\:{taken}\:{it}\:\mathrm{100\%}. \\ $$