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Category: Probability and Statistics

An-urn-contains-24-balls-6-white-6-black-6-green-and-6-red-If-4-balls-are-drawn-at-random-with-replacement-What-is-the-probability-that-at-least-3-different-colors-are-represented-in-the-

Question Number 133818 by bramlexs22 last updated on 24/Feb/21 $$\mathrm{An}\:\mathrm{urn}\:\mathrm{contains}\:\mathrm{24}\:\mathrm{balls}\::\:\mathrm{6}\:\mathrm{white}\:,\:\mathrm{6}\:\mathrm{black},\: \\ $$$$\mathrm{6}\:\mathrm{green}\:,\:\mathrm{and}\:\mathrm{6}\:\mathrm{red}.\:\mathrm{If}\:\mathrm{4}\:\mathrm{balls}\: \\ $$$$\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random}\:\mathrm{with}\:\mathrm{replacement} \\ $$$$.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{different}\:\mathrm{colors}\:\mathrm{are}\: \\ $$$$\mathrm{represented}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sample}\:? \\ $$ Terms of Service…

A-test-consists-of-four-questions-each-of-which-contains-five-alternative-answers-one-of-which-is-correct-The-test-pass-condition-is-at-least-four-correct-answers-A-student-not-knowing-the-test-su

Question Number 133696 by Mikael_786 last updated on 23/Feb/21 $$\mathrm{A}\:\mathrm{test}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{four}\:\mathrm{questions} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{contains}\:\mathrm{five}\:\mathrm{alternative} \\ $$$$\mathrm{answers},\:\mathrm{one}\:\mathrm{of}\:\mathrm{which}\:\mathrm{is}\:\mathrm{correct}. \\ $$$$\mathrm{The}\:\mathrm{test}\:\mathrm{pass}\:\mathrm{condition}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{four}\:\mathrm{correct}\:\mathrm{answers}.\:\mathrm{A}\:\mathrm{student},\:\mathrm{not} \\ $$$$\mathrm{knowing}\:\mathrm{the}\:\mathrm{test}\:\mathrm{subject},\:\mathrm{scored}\:\mathrm{the} \\ $$$$\mathrm{answers}\:\mathrm{randomly}.\mathrm{How}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{for}\:\mathrm{the}\:\mathrm{student}\:\mathrm{to}\:\mathrm{pass}? \\…

If-you-have-n-non-parallel-lines-in-a-plane-how-many-points-of-intersection-are-there-

Question Number 2621 by Yozzi last updated on 23/Nov/15 $${If}\:{you}\:{have}\:{n}\:{non}−{parallel} \\ $$$${lines}\:{in}\:{a}\:{plane},\:{how}\:{many}\:{points} \\ $$$${of}\:{intersection}\:{are}\:{there}? \\ $$ Answered by prakash jain last updated on 23/Nov/15 $$\mathrm{Choose}\:\mathrm{any}\:\mathrm{2}\:\mathrm{lines}\:\mathrm{and}\:\mathrm{we}\:\mathrm{get}\:\mathrm{point}\:\mathrm{of}…

Given-10-white-balls-and-ten-black-balls-numbered-1-2-10-How-many-ways-can-we-choose-6-balls-such-that-i-no-two-chosen-balls-have-the-same-number-ii-two-pairs-of-chosen-balls-have-the-same-n

Question Number 133424 by liberty last updated on 22/Feb/21 $$\mathrm{Given}\:\mathrm{10}\:\mathrm{white}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{ten}\:\mathrm{black}\:\mathrm{balls} \\ $$$$\mathrm{numbered}\:\mathrm{1},\mathrm{2},…,\mathrm{10}.\:\mathrm{How}\:\mathrm{many}\: \\ $$$$\mathrm{ways}\:\mathrm{can}\:\mathrm{we}\:\mathrm{choose}\:\mathrm{6}\:\mathrm{balls}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{no}\:\mathrm{two}\:\mathrm{chosen}\:\mathrm{balls}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{number} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{two}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{chosen}\:\mathrm{balls}\:\mathrm{have} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{number}? \\ $$ Answered by EDWIN88…

Let-A-denote-the-event-of-test-positive-in-a-specific-experiment-and-B-that-of-have-cancer-It-is-known-that-P-B-0-005-P-A-B-0-95-and-P-A-B-0-95-Suppose-someone-tests-positive-in-the

Question Number 133420 by liberty last updated on 22/Feb/21 $$\mathrm{Let}\:\mathrm{A}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{event}\:\mathrm{of}\:'\mathrm{test}\:\mathrm{positive}' \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{specific}\:\mathrm{experiment},\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{that}\:\mathrm{of}\:'\mathrm{have}\:\mathrm{cancer}'.\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that} \\ $$$$\mathrm{P}\left(\mathrm{B}\right)=\mathrm{0}.\mathrm{005}\:,\:\mathrm{P}\left(\mathrm{A}\mid\mathrm{B}\right)=\:\mathrm{0}.\mathrm{95}\:\mathrm{and}\:\mathrm{P}\left(\overset{−} {\mathrm{A}}\mid\overset{−} {\mathrm{B}}\right)=\:\mathrm{0}.\mathrm{95} \\ $$$$\mathrm{Suppose}\:\mathrm{someone}\:\mathrm{tests}\:\mathrm{positive}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{experiment}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{he}\:\mathrm{has}\:\mathrm{cancer}\:. \\…

A-multiple-choice-quiz-has-200-questions-each-with-4-possible-answers-of-which-only-1-is-the-correct-answer-What-is-the-probability-that-sheer-guesswork-yields-from-25-to-30-correct-answer-for-8

Question Number 133021 by liberty last updated on 18/Feb/21 $$\mathrm{A}\:\mathrm{multiple}\:−\mathrm{choice}\:\mathrm{quiz}\:\mathrm{has}\:\mathrm{200} \\ $$$$\mathrm{questions}\:\mathrm{each}\:\mathrm{with}\:\mathrm{4}\:\mathrm{possible}\: \\ $$$$\mathrm{answers}\:\mathrm{of}\:\mathrm{which}\:\mathrm{only}\:\mathrm{1}\:\mathrm{is}\:\mathrm{the}\:\mathrm{correct} \\ $$$$\mathrm{answer}\:.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\: \\ $$$$\mathrm{that}\:\mathrm{sheer}\:\mathrm{guesswork}\:\mathrm{yields}\: \\ $$$$\mathrm{from}\:\mathrm{25}\:\mathrm{to}\:\mathrm{30}\:\mathrm{correct}\:\mathrm{answer}\:\mathrm{for} \\ $$$$\mathrm{80}\:\mathrm{of}\:\mathrm{the}\:\mathrm{200}\:\mathrm{problems}\:\mathrm{about}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{student}\:\mathrm{has}\:\mathrm{no}\:\mathrm{knowledge}?\: \\…

John-and-Ghina-have-a-date-at-a-given-time-and-each-will-arrive-at-the-meeting-place-with-a-delay-between-0-and-1-hour-with-all-pairs-of-delays-being-equally-likely-The-first-arrive-will-wait-for-1

Question Number 132548 by liberty last updated on 15/Feb/21 $$\mathrm{John}\:\mathrm{and}\:\mathrm{Ghina}\:\mathrm{have}\:\mathrm{a}\:\mathrm{date}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{given}\:\mathrm{time},\:\mathrm{and}\:\mathrm{each}\:\mathrm{will}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{meeting}\:\mathrm{place}\:\mathrm{with}\:\mathrm{a}\:\mathrm{delay}\:\mathrm{between} \\ $$$$\mathrm{0}\:\mathrm{and}\:\mathrm{1}\:\mathrm{hour},\:\mathrm{with}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of} \\ $$$$\mathrm{delays}\:\mathrm{being}\:\mathrm{equally}\:\mathrm{likely}. \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{arrive}\:\mathrm{will}\:\mathrm{wait}\:\mathrm{for} \\ $$$$\mathrm{15}\:\mathrm{minutes}\:\mathrm{and}\:\mathrm{will}\:\mathrm{leave}\:\mathrm{if} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{has}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{arrived}.\:\mathrm{What} \\…

A-conservative-design-team-call-it-C-and-innovative-design-team-call-it-N-are-asked-to-separately-design-a-new-product-within-a-month-From-past-experience-we-know-that-a-The-probability-that-te

Question Number 132551 by liberty last updated on 15/Feb/21 $$\mathrm{A}\:\mathrm{conservative}\:\mathrm{design}\:\mathrm{team}\:,\:\mathrm{call}\:\mathrm{it}\:\mathrm{C} \\ $$$$\mathrm{and}\:\mathrm{innovative}\:\mathrm{design}\:\mathrm{team}\:\mathrm{call} \\ $$$$\mathrm{it}\:\mathrm{N}\:,\:\mathrm{are}\:\mathrm{asked}\:\mathrm{to}\:\mathrm{separately}\:\mathrm{design} \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{product}\:\mathrm{within}\:\mathrm{a}\:\mathrm{month}. \\ $$$$\mathrm{From}\:\mathrm{past}\:\mathrm{experience}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{C}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{is}\:\mathrm{2}/\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{N}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{1}/\mathrm{2} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\…