3: Mada ya uwezekano
- Page ID
- 179601
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Una, zaidi ya uwezekano, uwezekano uliotumiwa. Kwa kweli, labda una hisia ya angavu ya uwezekano. Uwezekano unahusika na nafasi ya tukio linalotokea. Wakati wowote unapopima tabia mbaya ya kufanya kazi yako ya nyumbani au kujifunza kwa mtihani, unatumia uwezekano. Katika sura hii, utajifunza jinsi ya kutatua matatizo ya uwezekano kwa kutumia mbinu ya utaratibu.
- 3.0: Utangulizi wa Uwezekano
- Mara nyingi ni muhimu “nadhani” kuhusu matokeo ya tukio ili kufanya uamuzi. Wanasiasa wanasoma uchaguzi kubahatisha uwezekano wao wa kushinda uchaguzi. Walimu huchagua kozi fulani ya kujifunza kulingana na kile wanachofikiri wanafunzi wanaweza kuelewa. Madaktari huchagua matibabu yanayohitajika kwa magonjwa mbalimbali kulingana na tathmini yao ya matokeo ya uwezekano. Unaweza kuwa alitembelea casino ambapo watu kucheza michezo waliochaguliwa kwa sababu ya imani kwamba uwezekano wa kushinda ni nzuri.
- 3.4: Meza ya Dharura na Miti ya uwezekano
- Jedwali la dharura hutoa njia ya kuonyesha data ambayo inaweza kuwezesha kuhesabu probabilities. Jedwali husaidia katika kuamua uwezekano wa masharti kwa urahisi kabisa. Jedwali linaonyesha maadili ya sampuli kuhusiana na vigezo viwili tofauti ambavyo vinaweza kutegemeana au vinavyotegemea.
- 3.5: Venn michoro
- Mchoro wa Venn ni picha ambayo inawakilisha matokeo ya majaribio. Kwa ujumla lina sanduku ambalo linawakilisha nafasi ya sampuli S pamoja na miduara au ovals. Miduara au ovals inawakilisha matukio. Venn michoro pia kutusaidia kubadilisha maneno ya kawaida ya Kiingereza katika maneno ya hisabati ambayo kusaidia kuongeza usahihi.