Thaum xam qhov sib txawv, koj tab tom sim txiav txim siab qhov tshwm sim ntawm qhov xwm txheej tshwm sim rau tus lej ntawm kev sim. Qhov yuav tshwm sim yog qhov yuav tshwm sim uas ib lossis ntau qhov xwm txheej yuav tshwm sim faib los ntawm tus lej ntawm qhov ua tau. Kev suav qhov tshwm sim ntawm tshwm sim ntawm ntau qhov xwm txheej tau ua los ntawm kev faib cov teeb meem mus rau ntau qhov tshwm sim thiab muab lawv los ntawm ib leeg.
Kauj ruam
Txoj Kev 1 ntawm 3: Nrhiav Qhov Zoo Ntawm Ib Qhov Kev tshwm sim Random
Kauj Ruam 1. Xaiv cov xwm txheej nrog qhov ua tau tshwj xeeb
Qhov sib txawv tsuas yog xam thaum qhov xwm txheej (uas qhov sib txawv tau suav) tshwm sim lossis tsis tshwm sim. Cov xwm txheej thiab lawv qhov kev tawm tsam tsis tuaj yeem tshwm sim tib lub sijhawm. Dov tus lej 5 ntawm tsuav, tus nees uas yeej qhov kev sib tw, yog ib qho piv txwv ntawm ib qho kev tshwm sim tshwj xeeb. Koj yog tus lej 5, lossis koj tsis ua; koj tus nees yeej qhov kev sib tw, lossis tsis yog.
Piv txwv:
Nws tsis yooj yim sua kom xam qhov tshwm sim ntawm qhov tshwm sim: "Tus lej 5 thiab 6 yuav tshwm rau ntawm ib lub yob ntawm tsuav."
Kauj Ruam 2. Txheeb xyuas txhua qhov xwm txheej thiab cov txiaj ntsig uas tuaj yeem tshwm sim
Hais tias koj tab tom sim nrhiav qhov tshwm sim ntawm kev tau txais tus lej 3 thiab 6 ntawm cov tsuav. "Dov tus lej 3" yog qhov xwm txheej, thiab txij li 6-tog tuag tuaj yeem ua ib qho ntawm tus lej 1-6, tus lej ntawm cov txiaj ntsig yog 6. Yog li, hauv qhov no peb paub tias muaj 6 qhov ua tau tshwm sim thiab 1 qhov xwm txheej uas peb xav tau suav. Nov yog 2 qhov piv txwv los pab koj:
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Piv txwv 1: Dab tsi yog qhov yuav tshwm sim ntawm ib hnub uas poob rau hnub so thaum xaiv ib hnub ntawm kev xaiv?
"Xaiv ib hnub uas poob rau hnub so" yog qhov xwm txheej, thiab tus naj npawb ntawm cov txiaj ntsig yog hnub tag nrho ntawm lub lim tiam, uas yog 7.
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Piv txwv 2: Lub thawv muaj 4 pob zeb xiav, 5 pob zeb liab, thiab 11 pob zeb dawb. Yog tias ib lub pob zeb marble tau kos los ntawm lub thawv ntawm qhov tsis sib xws, qhov yuav tshwm sim li cas yog tias cov pob zeb liab tau kos?
"Xaiv cov pob zeb liab" yog peb qhov xwm txheej, thiab tus naj npawb ntawm cov txiaj ntsig yog tag nrho cov pob zeb pob zeb hauv lub thawv, uas yog 20.
Kauj Ruam 3. Sib faib cov xwm txheej los ntawm tag nrho cov txiaj ntsig
Qhov kev suav no yuav qhia qhov tshwm sim uas yuav tshwm sim ib zaug. Nyob rau hauv cov ntaub ntawv ntawm dov ib 3 ntawm 6-sided tuag, tus naj npawb ntawm cov xwm txheej yog 1 (muaj tsuas yog ib qho 3 hauv qhov tuag), thiab tus naj npawb ntawm cov txiaj ntsig yog 6. Koj tuaj yeem nthuav qhia qhov kev sib raug zoo no li 16, 1 /6, 0, 166, lossis 16, 6%. Txheeb xyuas qee qhov piv txwv hauv qab no:
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Piv txwv 1: Dab tsi yog qhov yuav tshwm sim ntawm ib hnub uas poob rau hnub so thaum xaiv ib hnub ntawm kev xaiv?
Tus naj npawb ntawm cov xwm txheej yog 2 (txij li hnub so muaj 2 hnub), thiab tus naj npawb ntawm cov txiaj ntsig yog 7. Qhov tshwm sim yog 2 7 = 2/7. Koj tseem tuaj yeem nthuav nws li 0.285 lossis 28.5%.
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Piv txwv 2: Lub thawv muaj 4 pob zeb xiav, 5 pob zeb liab, thiab 11 pob zeb dawb. Yog tias ib lub pob zeb marble tau kos los ntawm lub thawv ntawm qhov tsis sib xws, qhov yuav tshwm sim li cas yog tias cov pob zeb liab tau kos?
Tus naj npawb ntawm cov xwm txheej yog 5 (txij li muaj 5 pob zeb liab liab), thiab cov txiaj ntsig ntawm qhov tshwm sim yog 20. Yog li, qhov tshwm sim yog 5 20 = 1/4. Koj tseem tuaj yeem qhia nws ua 0, 25 lossis 25%.
Kauj Ruam 4. Ntxiv txhua qhov xwm txheej tshwm sim kom ntseeg tau tias lawv sib npaug 1
Qhov yuav tshwm sim ntawm txhua qhov xwm txheej yuav tsum mus txog 1 aka 100%. Yog tias qhov sib txawv tsis mus txog 100%, nws zoo li koj tau ua yuam kev vim tias muaj qhov xwm txheej tsis zoo. Muab ob npaug rau txheeb xyuas koj cov laij lej rau qhov ua yuam kev.
Piv txwv li, koj qhov tshwm sim ntawm kev tau txais 3 thaum koj yob 6-sided tuag yog 1/6. Txawm li cas los xij, qhov sib txawv ntawm dov lwm tsib tus lej ntawm cov tsuav kuj yog 1/6. 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6, uas yog sib npaug 100%
Sau ntawv:
Piv txwv li, yog tias koj tsis nco qab suav nrog qhov sib txawv ntawm tus lej 4 ntawm cov tsuav, qhov sib txawv tag nrho tsuas yog 5/6 lossis 83%, qhia qhov ua yuam kev.
Kauj Ruam 5. Muab 0 rau lub caij nyoog tsis yooj yim sua
Qhov no txhais tau tias qhov xwm txheej yuav tsis muaj tseeb, thiab tshwm sim txhua lub sijhawm koj ua qhov xwm txheej yuav los. Thaum xam 0 qhov sib txawv yog qhov tsawg, nws tsis yooj yim ib yam.
Piv txwv li, yog tias koj xam qhov tshwm sim uas hnub so Easter poob rau hnub Monday xyoo 2020, qhov tshwm sim yog 0 vim tias Easter ib txwm ua kev zoo siab rau hnub Sunday
Txoj Kev 2 ntawm 3: Xam qhov yuav tshwm sim ntawm ntau yam xwm txheej tsis xwm txheej
Kauj Ruam 1. Saib xyuas txhua lub sijhawm cais los xam cov xwm txheej ywj pheej
Thaum koj paub tias qhov sib txawv ntawm txhua qhov xwm txheej yog dab tsi, suav lawv cais. Hais tias koj xav paub qhov tshwm sim ntawm dov tus lej 5 ob zaug uake ntawm 6-sided tuag. Thawj qhov tshwm sim tsis cuam tshuam nrog qhov tshwm sim thib ob.
Sau ntawv:
Qhov tshwm sim ntawm kev tau txais tus lej 5 yog hu ua kev tshwm sim ywj pheej vim tias dab tsi tshwm sim thawj zaug tsis cuam tshuam dab tsi tshwm sim zaum ob.
Kauj Ruam 2. Xav txog qhov cuam tshuam ntawm cov xwm txheej yav dhau los thaum xam cov xwm txheej sib xws
Yog tias qhov tshwm sim ntawm ib qho xwm txheej hloov pauv qhov tshwm sim ntawm qhov xwm txheej thib ob, koj tab tom xam qhov tshwm sim kev tshwm sim nyob ntawm. Piv txwv li, yog tias koj muaj 2 daim npav los ntawm ib lub lawj ntawm 52 daim npav, thaum koj xaiv thawj daim npav, qhov no cuam tshuam qhov txawv ntawm daim npav uas tuaj yeem rub tawm ntawm lub lawj. Txhawm rau xam qhov tshwm sim ntawm daim npav thib ob los ntawm ob qhov xwm txheej sib xws, rho tus lej ntawm qhov ua tau los ntawm 1 thaum xam qhov tshwm sim ntawm qhov xwm txheej thib ob.
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Piv txwv 1: Xav txog qhov tshwm sim: Ob daim npav raug rho tawm ntawm daim npav npav. Dab tsi yog qhov tshwm sim uas ob leeg yog daim npav ntawm spades?
Qhov txawv ntawm thawj daim npav uas muaj tus cim spade yog 13/52, lossis 1/4. (Muaj 13 daim npav ntawm spades hauv daim npav ua tiav).
Tam sim no, qhov tshwm sim ntawm daim npav thib ob uas muaj tus cim spade yog 12/51 vim tias 1 ntawm tus spades twb tau kos lawm. Yog li, thawj qhov xwm txheej cuam tshuam rau qhov tshwm sim thib ob. Yog tias koj kos 3 ntawm spades thiab tsis muab nws rov qab rau hauv lub lawj, nws txhais tau tias daim npav pob thiab lub lawj tag nrho tau raug txo los ntawm 1 (51 tsis yog 52)
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Piv txwv 2: Lub thawv muaj 4 pob zeb xiav, 5 pob zeb liab, thiab 11 pob zeb dawb. Yog tias 3 pob zeb tau kos los ntawm lub raj mis, yuav ua li cas thiaj li yuav tau pob zeb liab, pob zeb xiav thib ob, thiab pob zeb dawb thib peb tau kos?
Qhov tshwm sim ntawm kev kos duab liab marble thawj zaug yog 5/20, lossis 1/4. Qhov tshwm sim ntawm kev kos xim xiav rau cov pob zeb thib ob yog 4/19 vim tias tag nrho cov pob zeb pob zeb hauv lub thawv tau txo los ntawm ib qho, tab sis tus lej ntawm cov pob zeb xiav tsis tau poob. Thaum kawg, qhov tshwm sim tias qhov thib peb marble yog dawb yog 11/18 vim tias koj twb tau xaiv 2 pob zeb pob zeb
Kauj Ruam 3. Muab qhov yuav tshwm sim ntawm txhua qhov xwm txheej cais los ntawm ib leeg
Txawm hais tias koj tab tom ua haujlwm ntawm cov xwm txheej ywj pheej lossis vam khom, thiab tus naj npawb ntawm cov txiaj ntsig tau koom nrog yog 2, 3, lossis txawm tias 10, koj tuaj yeem suav qhov tshwm sim tag nrho los ntawm kev sib kis cov xwm txheej cais no. Qhov tshwm sim yog qhov tshwm sim ntawm ntau qhov xwm txheej tshwm sim ib tug tom qab lwm tus. Yog li, rau qhov xwm txheej no, qhov xwm txheej zoo li cas uas koj yuav yob 5 hauv ib kab rau ntawm rau sab tuag? Qhov tshwm sim uas ib yob ntawm tus lej 5 tshwm sim yog 1/6. Yog li, koj suav 1/6 x 1/6 = 1/36. Koj tseem tuaj yeem qhia nws ua tus lej lej ntawm 0.027 lossis feem pua ntawm 2.7%.
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Piv txwv 1: Ob daim npav raug rub los ntawm lub lawj ntawm qhov tsis raug. Dab tsi yog qhov tshwm sim uas ob daim npav muaj tus cim spade?
Qhov tshwm sim ntawm thawj qhov tshwm sim tshwm sim yog 13/52. Qhov tshwm sim ntawm qhov xwm txheej thib ob tshwm sim yog 12/51. Qhov tshwm sim ntawm ob qho yog 13/52 x 12/51 = 12/204 = 1/17. Koj tuaj yeem nthuav qhia nws li 0.058 lossis 5.8%.
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Piv txwv 2: Lub thawv uas muaj 4 pob zeb xiav, 5 pob zeb liab, thiab 11 pob zeb dawb. Yog tias peb pob zeb pob zeb tau rub los ntawm lub thawv ntawm qhov tsis sib xws, qhov yuav tshwm sim tau li cas yog tias thawj cov pob zeb liab yog xim liab, qhov thib ob yog xiav, thiab qhov thib peb yog dawb?
Qhov tshwm sim ntawm thawj qhov tshwm sim yog 5/20. Qhov tshwm sim ntawm qhov xwm txheej thib ob yog 4/19. Thaum kawg, qhov sib txawv ntawm qhov xwm txheej thib peb yog 11/18. Qhov sib txawv tag nrho yog 5/20 x 4/19 x 11/18 = 44/1368 = 0.032. Koj tseem tuaj yeem hais nws li 3.2%.
Txoj Kev 3 ntawm 3: Hloov Txoj Hauv Kev Rau Qhov Muaj Peev Xwm
Kauj Ruam 1. Qhia qhov tshwm sim raws li qhov piv nrog qhov ua tau zoo raws li tus lej
Piv txwv li, cia saib dua ntawm qhov piv txwv ntawm lub thawv uas muaj cov xim pob zeb ci. Hais tias koj xav paub qhov tshwm sim uas koj yuav kos cov pob zeb dawb (uas muaj 11), los ntawm tag nrho cov pob zeb pob zeb hauv lub thawv (uas muaj 20). Qhov tshwm sim ntawm qhov xwm txheej tshwm sim yog qhov piv ntawm qhov tshwm sim ntawm qhov xwm txheej yuav tshwm sim rau qhov yuav tshwm sim yuav tsis tshwm sim Txij li thaum muaj 11 pob zeb pob zeb dawb thiab 9 pob zeb tsis dawb, qhov sib txawv tau sau hauv qhov sib piv 11: 9.
- Tus lej 11 sawv cev rau qhov yuav tshwm sim ntawm kev kos duab marble dawb thiab tus lej 9 sawv cev rau qhov yuav tshwm sim ntawm kev kos duab marble ntawm lwm xim.
- Yog li, koj txoj hauv kev rub cov pob zeb dawb yog qhov siab heev.
Kauj Ruam 2. Ntxiv cov zauv los hloov qhov yuav muaj tseeb
Hloov qhov txawv yuav yooj yim heev. Ua ntej, ua txhaum qhov tshwm sim rau hauv 2 qhov xwm txheej sib cais: qhov yuav tshwm sim ntawm kos cov pob zeb dawb (11) thiab qhov tshwm sim ntawm kev kos lwm lub pob zeb marble (9). Ntxiv cov lej ua ke los xam tag nrho cov txiaj ntsig. Sau nws raws li qhov tshwm sim, nrog tus lej tshiab suav los ua tus lej.
Tus naj npawb ntawm cov txiaj ntsig los ntawm qhov xwm txheej uas koj xaiv pob zeb dawb yog 11; tus naj npawb ntawm cov txiaj ntsig koj kos lwm yam xim yog 9. Yog li tag nrho cov txiaj ntsig yog 11 + 9, lossis 20
Kauj Ruam 3. Nrhiav qhov tshwm sim zoo li koj tab tom xam qhov tshwm sim ntawm ib qho xwm txheej
Koj tau pom tias muaj tag nrho 20 qhov muaj peev xwm ua tau, thiab 11 ntawm lawv yog los kos cov pob zeb dawb. Yog li, qhov tshwm sim ntawm kev kos duab marble dawb tam sim no tuaj yeem ua haujlwm zoo li cuam tshuam nrog qhov tshwm sim ntawm lwm qhov xwm txheej. Faib 11 (tus naj npawb ntawm cov txiaj ntsig zoo) los ntawm 20 (tag nrho cov xwm txheej) kom tau txais qhov tshwm sim.
Yog li, hauv peb qhov piv txwv, qhov tshwm sim ntawm kev kos cov pob zeb dawb yog 11/20. Sib faib cov feem: 11 20 = 0.55 lossis 55%
Lub tswv yim
- Cov lej zauv feem ntau siv lo lus "txheeb ze zaus" txhawm rau txheeb xyuas qhov tshwm sim uas yuav tshwm sim. Lo lus "txheeb ze" tau siv vim tias tsis muaj txiaj ntsig tau 100% lav. Piv txwv li, yog tias koj npib ib npib 100 zaug, ua tau Koj yuav tsis tau txais 50 sab ntawm tus lej thiab 50 sab ntawm lub logo. Cov txheeb ze sib txawv kuj coj qhov no mus rau hauv tus account.
- Qhov tshwm sim ntawm qhov xwm txheej tsis tuaj yeem yog tus lej tsis zoo. Yog tias koj tau txais tus lej tsis zoo, rov tshuaj xyuas koj ob npaug.
- Feem ntau txoj hauv kev nthuav qhia qhov sib txawv yog nrog cov zauv, zauv zauv, feem pua, lossis qib 1-10.
- Koj yuav tsum paub tias hauv kev ncaws pob ncaws pob, qhov sib txawv tau hais raws li "qhov tsis sib xws" (qhov sib txawv tawm tsam), uas txhais tau tias qhov sib txawv ntawm qhov xwm txheej tshwm sim tau teev tseg ua ntej, thiab qhov sib txawv ntawm qhov xwm txheej tsis tshwm sim tau teev tseg tom qab. Txawm hais tias nws tuaj yeem ua rau tsis meej pem qee lub sijhawm, koj yuav tsum paub yog tias koj xav sim koj txoj hmoov ntawm kev sib tw ncaws pob.
