Question Number 133293 by liberty last updated on 21/Feb/21 Commented by mr W last updated on 21/Feb/21 $${what}\:{is}\:{the}\:\mathrm{3}{rd}\:{category}? \\ $$$${office}\:{related}\:{books}, \\ $$$${literature}\:{book}, \\ $$$${and}\:{what}\:{else}? \\…
Question Number 133021 by liberty last updated on 18/Feb/21 $$\mathrm{A}\:\mathrm{multiple}\:−\mathrm{choice}\:\mathrm{quiz}\:\mathrm{has}\:\mathrm{200} \\ $$$$\mathrm{questions}\:\mathrm{each}\:\mathrm{with}\:\mathrm{4}\:\mathrm{possible}\: \\ $$$$\mathrm{answers}\:\mathrm{of}\:\mathrm{which}\:\mathrm{only}\:\mathrm{1}\:\mathrm{is}\:\mathrm{the}\:\mathrm{correct} \\ $$$$\mathrm{answer}\:.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\: \\ $$$$\mathrm{that}\:\mathrm{sheer}\:\mathrm{guesswork}\:\mathrm{yields}\: \\ $$$$\mathrm{from}\:\mathrm{25}\:\mathrm{to}\:\mathrm{30}\:\mathrm{correct}\:\mathrm{answer}\:\mathrm{for} \\ $$$$\mathrm{80}\:\mathrm{of}\:\mathrm{the}\:\mathrm{200}\:\mathrm{problems}\:\mathrm{about}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{student}\:\mathrm{has}\:\mathrm{no}\:\mathrm{knowledge}?\: \\…
Question Number 132548 by liberty last updated on 15/Feb/21 $$\mathrm{John}\:\mathrm{and}\:\mathrm{Ghina}\:\mathrm{have}\:\mathrm{a}\:\mathrm{date}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{given}\:\mathrm{time},\:\mathrm{and}\:\mathrm{each}\:\mathrm{will}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{meeting}\:\mathrm{place}\:\mathrm{with}\:\mathrm{a}\:\mathrm{delay}\:\mathrm{between} \\ $$$$\mathrm{0}\:\mathrm{and}\:\mathrm{1}\:\mathrm{hour},\:\mathrm{with}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of} \\ $$$$\mathrm{delays}\:\mathrm{being}\:\mathrm{equally}\:\mathrm{likely}. \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{arrive}\:\mathrm{will}\:\mathrm{wait}\:\mathrm{for} \\ $$$$\mathrm{15}\:\mathrm{minutes}\:\mathrm{and}\:\mathrm{will}\:\mathrm{leave}\:\mathrm{if} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{has}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{arrived}.\:\mathrm{What} \\…
Question Number 132551 by liberty last updated on 15/Feb/21 $$\mathrm{A}\:\mathrm{conservative}\:\mathrm{design}\:\mathrm{team}\:,\:\mathrm{call}\:\mathrm{it}\:\mathrm{C} \\ $$$$\mathrm{and}\:\mathrm{innovative}\:\mathrm{design}\:\mathrm{team}\:\mathrm{call} \\ $$$$\mathrm{it}\:\mathrm{N}\:,\:\mathrm{are}\:\mathrm{asked}\:\mathrm{to}\:\mathrm{separately}\:\mathrm{design} \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{product}\:\mathrm{within}\:\mathrm{a}\:\mathrm{month}. \\ $$$$\mathrm{From}\:\mathrm{past}\:\mathrm{experience}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{C}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{is}\:\mathrm{2}/\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{N}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{1}/\mathrm{2} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\…
Question Number 132086 by SLVR last updated on 11/Feb/21 $$ \\ $$ Commented by mr W last updated on 11/Feb/21 $${it}'{s}\:{getting}\:{boring}! \\ $$$${please}\:{stop}\:{posting}\:{empty}\:{posts}\:{sir}! \\ $$$${try}\:{to}\:{study}\:{how}\:{to}\:{use}\:{the}\:{forum}\:{by}…
Question Number 973 by Yugi last updated on 10/May/15 $${The}\:{number}\:{of}\:{hits}\:{per}\:{minute}\:{on}\:{a}\:{website}\:{is}\:\mathrm{0}.\mathrm{8}.\:{It}\:{is}\:{shown}\:{that}\:{the}\:{time}\:{T} \\ $$$${between}\:{two}\:{successive}\:{hits}\:{follows}\:{a}\:{negative}\:{exponential}\:{distribution}\: \\ $$$${f}\left({t}\right)=\mathrm{0}.\mathrm{8}{e}^{−\mathrm{0}.\mathrm{8}{t}} \:\left(\:{t}\:\geqslant\:\mathrm{0}\:\right).\:{It}\:{is}\:{required}\:{to}\:{determine}\:{the}\:{probability}\:{that}\:{the}\:{time}\: \\ $$$${between}\:{the}\:\mathrm{1}{st}\:{hit}\:{and}\:{the}\:\mathrm{51}{st}\:{exceeds}\:{one}\:{hour}.\:{One}\:{approach}\:{to}\:{the}\: \\ $$$${calculation}\:{stated}\:{that}\:{the}\:{required}\:{probability}\:{is}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{P}\left({no}.\:{of}\:{hits}\:{in}\:\mathrm{60}\:{mins}\:<\:\mathrm{50}\right)\:\:\:\:\:\:\:\:\:\:\:\left(\:\ast\:\right) \\ $$$${Can}\:{anyone}\:{explain}\:{to}\:{me}\:{why}\:{it}\:{is}\:{that} \\ $$$${P}\left({time}\:{between}\:\mathrm{1}{st}\:{hit}\:{and}\:\mathrm{51}{st}\:{hit}\:>\:\mathrm{60}{mins}\right)=\:\left(\ast\right)\:?…
Question Number 131975 by liberty last updated on 10/Feb/21 $$\:\mathrm{Ninety}\:\mathrm{students}\:,\:\mathrm{including}\:\mathrm{Joe} \\ $$$$\mathrm{and}\:\mathrm{Jane}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{split}\:\mathrm{into}\: \\ $$$$\mathrm{three}\:\mathrm{classes}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{size}\:\mathrm{and}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{done}\:\mathrm{at}\:\mathrm{random}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{Joe}\:\mathrm{and}\:\mathrm{Jane} \\ $$$$\mathrm{end}\:\mathrm{up}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{class}\:? \\ $$ Commented by liberty…
Question Number 870 by 112358 last updated on 05/Apr/15 $${In}\:{how}\:{many}\:{ways}\:{may}\:{a}\:{line}\: \\ $$$${consisting}\:{of}\:\mathrm{4}\:{men}\:{and}\:\mathrm{4}\:{women} \\ $$$${be}\:{acquired}\:{if}\:{no}\:{two}\:{women}\:{are} \\ $$$${to}\:{be}\:{adjacent}\:{to}\:{each}\:{other}? \\ $$ Answered by prakash jain last updated on…
Question Number 131828 by Salman_Abir last updated on 09/Feb/21 Answered by liberty last updated on 09/Feb/21 $$\mathrm{20}\:=\:\frac{\mathrm{6}!}{\mathrm{3}!.\mathrm{3}!} \\ $$ Commented by Salman_Abir last updated on…
Question Number 683 by 112358 last updated on 24/Feb/15 $${Determine}\:{the}\:{following}\:{sum}\:{in} \\ $$$${terms}\:{of}\:{n}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}_{{n}} =\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}^{\mathrm{2}} {q}^{{i}−\mathrm{1}} \\ $$$${where}\:\mathrm{0}\:<\:{q}\:<\:\mathrm{1}. \\ $$$${For}\:{the}\:{distribution}\:{of}\:{the}\:{discrete} \\ $$$${random}\:{variable}\:{X}\:{given}\:{as} \\…