Category: Probability and Statistics

Question Number 135998 by nadovic last updated on 17/Mar/21 A  bowl contains carefully shredded confetti, 6 of which are blue and the remaining 12 are red.…

Question Number 4753 by FilupSmith last updated on 05/Mar/16 $$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\ast \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\ast \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\ast \\ $$$$ \\ $$$$\mathrm{Selecting}\:\mathrm{a}\:\mathrm{random}\:\mathrm{star}\:\mathrm{is}\:\mathrm{a}\:\:\frac{\mathrm{1}}{\mathrm{15}}\:\mathrm{chance} \\ $$$$\mathrm{at}\:\mathrm{random}.\:\mathrm{Lets}\:\mathrm{say}\:\mathrm{you}\:\mathrm{have}\:\mathrm{to}\:\mathrm{pick} \\ $$$$\mathrm{a}\:\mathrm{second}\:\mathrm{random}\:\mathrm{star}\:\mathrm{that}\:\mathrm{is}\:\mathrm{next}\:\mathrm{to}\:\mathrm{it}. \\ $$$${Either}\:{above},\:{below},\:{or}\:{to}\:{the}\:{side}. \\…

Question Number 4166 by Filup last updated on 30/Dec/15 Commented by prakash jain last updated on 31/Dec/15 $$\mathrm{To}\:\mathrm{go}\:\mathrm{broke}:\:{k}\:\mathrm{wins},\:\mathrm{2}+{k}\:\mathrm{losses} \\ $$$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{k}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}+{k}} =\:\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{\mathrm{1}−\frac{\mathrm{3}}{\mathrm{16}}}\:=\:\frac{\mathrm{1}}{\mathrm{13}}\:?…

Question Number 135181 by liberty last updated on 11/Mar/21 $$\mathrm{A}\:\mathrm{bag}\:\mathrm{has}\:\mathrm{4}\:\mathrm{red}\:\mathrm{marbles},\:\mathrm{5}\:\mathrm{white}\: \\ $$$$\mathrm{marbles}\:,\:\mathrm{and}\:\mathrm{6}\:\mathrm{blue}\:\mathrm{marbles}.\:\mathrm{Three} \\ $$$$\mathrm{marbles}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{from}\:\mathrm{the}\:\mathrm{bag},\:\left(\mathrm{without}\right. \\ $$$$\left.\mathrm{replacement}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{all}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}\:?\: \\ $$ Answered by EDWIN88 last updated…

Question Number 3894 by Filup last updated on 24/Dec/15 $$\mathrm{I}\:\mathrm{have}\:{n}\:\mathrm{six}\:\mathrm{sided}\:\mathrm{dice}. \\ $$$$\mathrm{I}\:\mathrm{roll}\:\mathrm{them}\:\mathrm{all}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{proability} \\ $$$$\mathrm{that}\:{k}\:\mathrm{of}\:\mathrm{them}\:\mathrm{share}\:\mathrm{the}\:\mathrm{same}\:\mathrm{value}? \\ $$ Commented by Filup last updated on 24/Dec/15 $$\mathrm{Whoops}.\:\mathrm{That}\:\mathrm{was}\:\mathrm{my}\:\mathrm{mistake}! \\…