Piv txwv ntawm Cov Lus Nug Sib Tham txog Qhov Feem Yuav Muaj Ib Qho Xwm Txheej
Qhov muaj feem yuav tshwm sim yog ib ceg ntawm kev suav lej uas siv dav hauv lub neej txhua hnub. Qhov muaj feem yuav tshwm sim lossis tsis tshwm sim tuaj yeem ntsuas tau siv lub tswv yim ntawm qhov muaj feem yuav tshwm sim. Tsab xov xwm hauv qab no yuav tham txog ntau qhov teeb meem piv txwv thiab lawv cov kev sib tham txog qhov muaj feem yuav tshwm sim. Cia peb tshuaj xyuas lawv kom tob dua.
Lo lus nug 1: Qhov feem pua ntawm cov lej yuav tshwm sim ntawm lub pob zeb
Lo lus nug:
Ib lub tuag uas muaj rau sab raug pov ib zaug. Muaj pes tsawg feem pua uas yuav tau 4?
Kev Sib Tham:
Ib lub tshuab tuag ib txwm muaj rau sab: 1, 2, 3, 4, 5, thiab 6. Txhua sab muaj feem sib npaug zos uas yuav tshwm sim. Vim peb tab tom nrhiav qhov feem pua ntawm kev dov tus lej 4 ntawm rau tus lej uas ua tau, qhov feem pua no tuaj yeem sau ua:
\[ P(4) = \frac{\text{Tus lej ntawm txoj kev xav tau}}{\text{Tag nrho cov peev xwm}} = \frac{1}{6} \]
Yog li ntawd, qhov feem pua ntawm kev tau tus lej 4 thaum pov ib lub tuag ib zaug yog \(\frac{1}{6}\).
Teeb Meem 2: Qhov Sib Tw Hauv Lub Thawv Kos
Lo lus nug:
Hauv ib lub thawv muaj 5 lub pob liab thiab 3 lub pob xiav. Yog tias lub pob raug kos tsis raws cai, qhov feem pua uas lub pob raug kos yog xim liab yog dab tsi?
Kev Sib Tham:
Tag nrho cov pob hauv lub thawv yog:
\[ 5 \text{ (liab) } + 3 \text{ (xiav) } = 8 \text{ pob } \]
Cov pob uas peb xav tau yog cov pob liab, uas muaj 5. Yog li, qhov feem pua ntawm kev tau txais pob liab yog:
\[ P(\text{liab}) = \frac{\text{Tus naj npawb ntawm cov pob liab}}{\text{Tag nrho cov pob}} = \frac{5}{8} \]
Yog li ntawd, qhov feem pua ntawm kev xaiv lub pob liab yog \(\frac{5}{8}\).
Lo lus nug 3: Qhov muaj feem yuav muaj taub hau ntawm lub npib
Lo lus nug:
Pov ib lub npib ob zaug. Muaj pes tsawg feem pua uas yuav tau ob lub taub hau?
Kev Sib Tham:
Txhua qhov pov npib muaj ob qho txiaj ntsig, uas yog taub hau (H) lossis tw (E). Thaum pov npib ob zaug, qhov chaw piv txwv (S) ntawm cov txiaj ntsig tau yog:
\[ S = \{(HH), (HE), (EH), (EE)\} \]
Qhov feem pua ntawm kev tau ob lub taub hau (HH) tuaj yeem suav raws li hauv qab no:
\[ P(HH) = \frac{\text{Tus lej ntawm HH cov xwm txheej}}{\text{Tag nrho cov peev xwm}} = \frac{1}{4} \]
Hauv lwm lo lus, qhov feem pua ntawm kev tau ob lub taub hau thaum lub npib raug pov ob zaug yog \(\frac{1}{4}\).
Lo lus nug 4: Qhov muaj feem yuav tshwm sim hauv kev ua si phaib
Lo lus nug:
Los ntawm ib pawg ntawv txheem (52 daim ntawv), yog tias kos ib daim ntawv, qhov feem pua ntawm kev tau txais Ace of Hearts yog dab tsi?
Kev Sib Tham:
Ib pawg ntawv txheem muaj 52 daim ntawv, suav nrog 4 Aces. Txawm li cas los xij, peb tsuas yog xav paub txog Ace of Hearts xwb.
Tag nrho cov ntawv ua tau yog 52, thiab tsuas muaj 1 Ace of Hearts hauv lub lawj. Yog li ntawd:
\[ P(\text{Ace ntawm Lub Siab}) = \frac{\text{Tus lej ntawm Aces ntawm Lub Siab}}{\text{Tag Nrho Tus lej ntawm Daim Npav}} = \frac{1}{52} \]
Yog li, qhov feem pua ntawm kev kos ib tug Ace ntawm lub plawv los ntawm ib pawg ntawv txheem yog \(\frac{1}{52}\).
Lo lus nug 5: Qhov sib txawv ntawm cov khoom muag
Lo lus nug:
Hauv ib daim lottery, muaj 10 daim pib, 3 daim muaj nqi zog thiab 7 daim tsis muaj nqi zog. Yog tias muaj ib daim pib raug rho tawm yam tsis tau npaj tseg, qhov feem pua ntawm kev yuav tau txais nqi zog yog dab tsi?
Kev Sib Tham:
Tag nrho cov pib yog 10, thiab tus lej ntawm cov pib khoom plig yog 3. Yog li, qhov muaj feem yuav tau txais daim pib khoom plig yog:
\[ P(\text{prize}) = \frac{\text{Tus lej ntawm daim pib khoom plig}}{\text{Tag nrho tus lej ntawm daim pib}} = \frac{3}{10} \]
Yog li ntawd, qhov feem pua ntawm kev tau txais daim pib khoom plig yog \(\frac{3}{10}\).
Lo lus nug 6: Qhov muaj feem yuav tshwm sim hauv lub thawv khoom qab zib
Lo lus nug:
Ib lub thawv muaj 12 lub khoom qab zib chocolate, 8 lub khoom qab zib strawberry, thiab 5 lub khoom qab zib mint. Yog tias ib lub khoom qab zib raug xaiv yam tsis tau npaj tseg, qhov feem pua ntawm kev tau txais ib lub khoom qab zib mint yog dab tsi?
Kev Sib Tham:
Tag nrho cov khoom qab zib hauv lub thawv yog:
\[ 12 \text{ (chocolate) } + 8 \text{ (strawberry) } + 5 \text{ (mint) } = 25 \text{ khoom qab zib} \]
Tus naj npawb ntawm cov khoom qab zib mint uas peb xav tau yog 5. Yog li ntawd, qhov muaj feem yuav tau txais cov khoom qab zib mint yog:
\[ P(\text{mint}) = \frac{\text{Tus lej ntawm cov mints}}{\text{Tag nrho cov mints}} = \frac{5}{25} = \frac{1}{5} \]
Yog li ntawd, qhov feem pua ntawm kev tau txais khoom qab zib mint yog \(\frac{1}{5}\).
Lo lus nug 7: Qhov sib txawv hauv Lottery
Lo lus nug:
Hauv kev rho npe, muaj 10 lub pob uas muaj tus lej 1 txog 10 muab tso rau hauv ib lub thawv. Yog tias muaj ib lub pob raug rho tawm, qhov feem pua ntawm kev yuav tau tus lej sib npaug yog dab tsi?
Kev Sib Tham:
Tag nrho cov pob yog 10 thiab cov lej sib npaug ntawm lawv yog 2, 4, 6, 8, thiab 10, uas tag nrho yog 5 lub pob.
Yog li ntawd, qhov feem pua ntawm kev tau txais tus lej sib npaug yog:
\[ P(\text{txawm}) = \frac{\text{Tus lej ntawm cov lej txawm}}{\text{Tag nrho cov pob}} = \frac{5}{10} = \frac{1}{2} \]
Yog li ntawd, qhov feem pua ntawm kev tau txais tus lej sib npaug yog \(\frac{1}{2}\).
Lo lus nug 8: Qhov sib txawv hauv kev sib tw
Lo lus nug:
Hauv kev ua si basketball, tus neeg ua si muaj 0,7 lub sijhawm los tau ib qho taw tes rau txhua qhov kev txhaj tshuaj. Yog tias tus neeg ua si ua 1 lub txhaj tshuaj, qhov feem pua uas nws yuav tsis tau yog dab tsi?
Kev Sib Tham:
Qhov feem pua ntawm kev ua tiav tau ib qho qhab nia yog 0,7. Yog li ntawd, qhov feem pua ntawm kev ua tsis tau ib qho qhab nia yog:
\[ P(\text{ua tsis tiav}) = 1 – P(\text{ua tiav}) = 1 – 0,7 = 0,3 \]
Yog li, lub sijhawm uas tus neeg ua si tsis tau qhab nia los ntawm ib qho pov yog 0,3 lossis 30%.
Tom qab peb tshuaj xyuas cov piv txwv thiab kev sib tham saum toj no, peb nkag siab tias lub tswv yim ntawm qhov muaj feem yuav siv tau li cas rau ntau yam xwm txheej thiab ntau yam. Qhov kev nkag siab no tuaj yeem pab daws cov teeb meem txhua hnub uas muaj kev tsis paub meej thiab kev kwv yees, thiab muab lub hauv paus ruaj khov rau kev siv ntxiv hauv kev kawm txog kev suav lej thiab qhov muaj feem yuav.
