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Category: Probability and Statistics

Given-three-events-A-B-and-C-sucb-that-P-A-P-C-P-A-C-1-10-P-A-C-1-2-P-C-B-2-7-P-B-C-4-5-find-a-P-A-b-P-B-

Question Number 76588 by Rio Michael last updated on 28/Dec/19 $$\mathrm{Given}\:\mathrm{three}\:\mathrm{events}\:\mathrm{A},\mathrm{B},\:\mathrm{and}\:\mathrm{C}\:\mathrm{sucb}\:\mathrm{that} \\ $$$$\mathrm{P}\left(\mathrm{A}\right)\:=\:\mathrm{P}\left(\mathrm{C}\right)\:,\:\mathrm{P}\left(\mathrm{A}\:\cap\:\mathrm{C}\right)\:=\:\frac{\mathrm{1}}{\mathrm{10}}\:,\:\mathrm{P}\left(\mathrm{A}\:\cup\:\mathrm{C}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{P}\left(\mathrm{C}\mid\mathrm{B}\right)\:=\:\frac{\mathrm{2}}{\mathrm{7}}\:\:,\:\mathrm{P}\left(\mathrm{B}\cup\mathrm{C}\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:\mathrm{find}\: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{P}\left(\mathrm{A}\right) \\ $$$$\left.\mathrm{b}\right)\:\mathrm{P}\left(\mathrm{B}\right) \\ $$ Answered by john santu…

Given-the-following-information-regarding-the-follwing-distribution-n-5-x-10-y-20-x-4-2-100-y-10-2-160-x-4-y-10-80-i-Find-the-two-regression-c

Question Number 10714 by Saham last updated on 23/Feb/17 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{following}\:\mathrm{information}\:\mathrm{regarding}\:\mathrm{the}\:\mathrm{follwing}\: \\ $$$$\mathrm{distribution}\::\:\: \\ $$$$\mathrm{n}\:=\:\mathrm{5},\:\:\:\:\overset{−} {\mathrm{x}}\:=\:\mathrm{10},\:\:\:\overset{−} {\mathrm{y}}\:=\:\mathrm{20},\:\:\:\Sigma\left(\mathrm{x}\:−\:\mathrm{4}\right)^{\mathrm{2}} \:=\:\mathrm{100},\:\:\Sigma\left(\mathrm{y}\:−\:\mathrm{10}\right)^{\mathrm{2}} \:=\:\mathrm{160}, \\ $$$$\Sigma\left(\mathrm{x}\:−\:\mathrm{4}\right)\left(\mathrm{y}\:−\:\mathrm{10}\right)\:=\:\mathrm{80} \\ $$$$\left(\mathrm{i}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{regression}\:\mathrm{coefficient}\:\mathrm{and} \\…

Daniel-and-Bruno-are-playing-with-perfect-cube-Daniel-is-the-first-player-if-he-obtains-1-or-2-he-wins-the-game-and-the-party-stopping-or-else-Bruno-plays-and-if-he-have-3-4-6-Bruno-won-and-the-game

Question Number 141692 by ArielVyny last updated on 22/May/21 $${Daniel}\:{and}\:{Bruno}\:{are}\:{playing}\:{with}\:{perfect}\:{cube} \\ $$$${Daniel}\:{is}\:{the}\:{first}\:{player}\:{if}\:{he}\:{obtains}\:\mathrm{1}\:{or}\:\mathrm{2} \\ $$$${he}\:{wins}\:{the}\:{game}\:{and}\:{the}\:{party}\:{stopping} \\ $$$${or}\:{else}\:{Bruno}\:{plays}\:{and}\:{if}\:{he}\:{have}\:\left\{\mathrm{3}.\mathrm{4}.\mathrm{6}\right\}\:{Bruno}\:{won}\:{and}\:{the}\:{game}\:{stopping} \\ $$$${Determine}\:{the}\:{probability}\:{that}\:{Daniel}\:{winand}\:{the}\:{probability}\:{that}\:{Bruno}\:{win} \\ $$$$ \\ $$ Answered by MJS_new…

1-lt-a-lt-b-prove-that-b-n-k-0-n-1-k-C-n-k-a-ln-p-0-n-k-C-n-k-p-a-n-p-b-p-ln-a-

Question Number 141633 by Willson last updated on 21/May/21 $$\mathrm{1}<\mathrm{a}<\mathrm{b}\:,\mathrm{prove}\:\mathrm{that}\:: \\ $$$${b}^{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \mathrm{C}_{{n}} ^{{k}} \:{a}^{\frac{{ln}\left(\underset{{p}=\mathrm{0}} {\overset{{n}−{k}} {\sum}}\mathrm{C}_{{n}−{k}} ^{{p}} {a}^{{n}−{p}} {b}^{{p}} \right)}{{ln}\left({a}\right)}} \\…

Prove-that-n-N-n-1-n-lnt-dt-ln-n-1-2-

Question Number 141409 by Willson last updated on 18/May/21 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\forall\mathrm{n}\in\mathbb{N}\:\:\:\:\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{lnt}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by TheSupreme last updated on 19/May/21 $$\int{ln}\left({t}\right)={xln}\left({t}\right)−{x} \\…

A-fair-die-is-thrown-4-times-What-is-the-probability-of-obtaining-a-6-twice-

Question Number 75802 by pete last updated on 17/Dec/19 $$\mathrm{A}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{4}\:\mathrm{times}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{of}\:\mathrm{obtaining}\:\mathrm{a}\:\mathrm{6}\:\mathrm{twice}? \\ $$ Answered by MJS last updated on 17/Dec/19 $$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\begin{pmatrix}{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}\:=\frac{\mathrm{25}}{\mathrm{216}}\approx\mathrm{11}.\mathrm{57\%} \\ $$ Commented…

what-is-the-probability-of-5-sundays-in-the-month-of-december-

Question Number 10116 by Gaurav3651 last updated on 25/Jan/17 $${what}\:{is}\:{the}\:{probability}\:{of}\:\mathrm{5}\:{sundays} \\ $$$${in}\:{the}\:{month}\:{of}\:{december}? \\ $$ Commented by prakash jain last updated on 25/Jan/17 $$\mathrm{Favorable}\:\mathrm{cases}−\:\mathrm{1}\:\mathrm{dec} \\ $$$$\mathrm{1}\:\mathrm{dec}\:\mathrm{Sunday}\Rightarrow\mathrm{1},\mathrm{8},\mathrm{15},\mathrm{22},\mathrm{29}\:\mathrm{are}\:\mathrm{sundays}…