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Category: Probability and Statistics

Roll-a-fair-die-twice-and-define-A-to-be-event-that-the-sum-of-the-scores-showing-up-is-greater-than-7-B-be-the-event-that-the-sum-of-the-scores-showing-up-is-a-multiple-of-3-and-C-be-the-event-that-

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Question Number 150030 by jlewis last updated on 08/Aug/21 $$\mathrm{Roll}\:\mathrm{a}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{twice}\:\mathrm{and}\:\mathrm{define}\:\mathrm{A}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{event}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing} \\ $$$$\mathrm{up}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{7},\:\mathrm{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}\:\mathrm{and}\:\mathrm{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{prime}\:\mathrm{number}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{events}\: \\ $$$$\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{independent}\:\mathrm{event}? \\…

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A-point-A-is-randomly-chosen-in-a-square-of-side-length-1-unit-Find-the-probability-the-distance-from-A-to-the-centre-of-the-square-does-not-exceed-x-

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Question Number 18945 by Tinkutara last updated on 01/Aug/17 $$\mathrm{A}\:\mathrm{point}\:'\mathrm{A}'\:\mathrm{is}\:\mathrm{randomly}\:\mathrm{chosen}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{square}\:\mathrm{of}\:\mathrm{side}\:\mathrm{length}\:\mathrm{1}\:\mathrm{unit}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{A}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exceed}\:\mathrm{x}. \\ $$ Commented by dioph last updated on 02/Aug/17…

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a-full-deck-of-52-cards-contains-13-hearts-Pick-8-cards-from-the-deck-at-random-without-replacement-what-is-the-probability-that-you-get-no-heart-

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Question Number 149981 by jlewis last updated on 08/Aug/21 $$\mathrm{a}\:\mathrm{full}\:\mathrm{deck}\:\mathrm{of}\:\mathrm{52}\:\mathrm{cards}\:\mathrm{contains}\:\mathrm{13} \\ $$$$\:\mathrm{hearts}.\:\mathrm{Pick}\:\mathrm{8}\:\mathrm{cards}\:\mathrm{from}\:\mathrm{the}\:\mathrm{deck} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{without}\:\mathrm{replacement}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{you}\:\mathrm{get} \\ $$$$\mathrm{no}\:\mathrm{heart}? \\ $$$$ \\ $$ Answered by mr…

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on-realise-une-suite-infinie-d-epreuves-independantes-chaque-epreuve-resulte-en-un-succes-avec-la-probabilite-p-0-1-ou-un-echec-avec-la-probabilite-q-1-p-soit-A-n-l-evement-obenir-au-moins-un-succ

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Question Number 149532 by ArielVyny last updated on 06/Aug/21 $${on}\:{realise}\:{une}\:{suite}\:{infinie}\:{d}'{epreuves} \\ $$$${independantes}.{chaque}\:{epreuve}\:{resulte}\:{en} \\ $$$$\left.{un}\:{succes}\:{avec}\:{la}\:{probabilite}\:{p}\in\right]\mathrm{0};\mathrm{1}\left[\:{ou}\:{un}\right. \\ $$$${echec}\:{avec}\:{la}\:{probabilite}\:{q}=\mathrm{1}−{p}.{soit}\:{A}_{{n}} \\ $$$${l}'{evement}\:“{obenir}\:{au}\:{moins}\:{un}\:{succes}\:{au} \\ $$$${cours}\:{des}\:{premieres}\:{epreuves}.''\:{determiner} \\ $$$${P}\left({A}_{{n}} \right) \\ $$…

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Question-149534

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Question Number 149534 by ArielVyny last updated on 06/Aug/21 Answered by Olaf_Thorendsen last updated on 06/Aug/21 $$\mathrm{Exercice}\:\mathrm{1}. \\ $$$$ \\ $$$$\mathrm{Loi}\:\mathrm{geometrique}\:\mathrm{P}\left(\mathrm{X}={k}\right)\:=\:{q}^{{k}−\mathrm{1}} {p} \\ $$$$\mathrm{La}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{repartition}\:\mathrm{est}\:: \\…

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on-distribue-au-hasard-8-boules-b-1-b-8-dans-6-tiroirs-t-1-t-6-soit-A-i-l-evenement-le-tiroir-t-i-est-vide-les-evenements-A-1-et-A-2-sont-ils-independants-

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Question Number 149471 by ArielVyny last updated on 05/Aug/21 $${on}\:{distribue}\:{au}\:{hasard}\:\mathrm{8}\:{boules}\:{b}_{\mathrm{1}} …{b}_{\mathrm{8}} \\ $$$${dans}\:\mathrm{6}\:{tiroirs}\:{t}_{\mathrm{1}} …{t}_{\mathrm{6}} .{soit}\:{A}_{{i}} \:{l}'{evenement} \\ $$$$“{le}\:{tiroir}\:{t}_{{i}} \:{est}\:{vide}''\:{les}\:{evenements}\:{A}_{\mathrm{1}} {et} \\ $$$${A}_{\mathrm{2}} {sont}-{ils}\:{independants}\:? \\ $$…

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Let-the-independent-random-variables-X-1-and-X-2-have-binomial-distribution-with-parameters-n-1-3-p-2-3-and-n-2-4-p-1-2-respectively-Compute-P-X-1-X-2-

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Question Number 149463 by jlewis last updated on 05/Aug/21 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{independent}\:\mathrm{random}\:\mathrm{variables} \\ $$$$\mathrm{X}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{X}_{\mathrm{2}} \:\mathrm{have}\:\mathrm{binomial}\:\mathrm{distribution} \\ $$$$\mathrm{with}\:\mathrm{parameters}\:\mathrm{n}_{\mathrm{1}} =\mathrm{3},\mathrm{p}=\mathrm{2}/\mathrm{3}\:\mathrm{and}\:\mathrm{n}_{\mathrm{2}} =\mathrm{4} \\ $$$$\mathrm{p}=\mathrm{1}/\mathrm{2}\:\:\mathrm{respectively}.\: \\ $$$$\mathrm{Compute}\:\mathrm{P}\left(\mathrm{X}_{\mathrm{1}} =\mathrm{X}_{\mathrm{2}} \right) \\…

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Question-149440

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Question Number 149440 by nadovic last updated on 05/Aug/21 Answered by Olaf_Thorendsen last updated on 07/Aug/21 $$\left(\mathrm{a}\right)\:\mathrm{A}_{\mathrm{1}} =\:“\mathrm{persons}\:\mathrm{from}\:\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{three} \\ $$$$\mathrm{groups}''. \\ $$$$\mathrm{That}\:\mathrm{means}\:\mathrm{3}\:\mathrm{volleyball}\:\mathrm{players}\:\mathrm{or} \\ $$$$\mathrm{3}\:\mathrm{hockey}\:\mathrm{players}. \\…

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