Question-209424

Question Number 209424 by Tawa11 last updated on 09/Jul/24

Commented by Tawa11 last updated on 09/Jul/24

In this kind of probability, is the formular. p(x = r) = ^n C_r p^r q^(n − r) or p(x = r) = ^n C_r q^r p^(n − r) ?????

$$\mathrm{In}\:\mathrm{this}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{probability},\:\mathrm{is}\:\mathrm{the}\:\mathrm{formular}. \\ $$$$\mathrm{p}\left(\mathrm{x}\:=\:\mathrm{r}\right)\:\:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \:\mathrm{p}^{\mathrm{r}} \:\mathrm{q}^{\mathrm{n}\:−\:\mathrm{r}} \\ $$$$\mathrm{or} \\ $$$$\mathrm{p}\left(\mathrm{x}\:=\:\mathrm{r}\right)\:\:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \:\mathrm{q}^{\mathrm{r}} \:\mathrm{p}^{\mathrm{n}\:−\:\mathrm{r}} \\ $$$$????? \\ $$

Commented by Tawa11 last updated on 09/Jul/24

$$\mathrm{Where}\:\:\:\mathrm{p}\:\:=\:\:\mathrm{success}\:\:\mathrm{and}\:\:\mathrm{q}\:\:=\:\:\mathrm{failure} \\ $$

Answered by mr W last updated on 09/Jul/24

(a) p=Σ_(r=2) ^(12) C_r ^(12) ×0.3^r ×0.7^(12−r) =0.915 (b) p=C_6 ^(12) ×0.3^6 ×0.7^6 =0.079 (c) p=Σ_(r=0) ^2 C_r ^(12) ×0.3^r ×0.7^(12−r) =0.253

$$\left({a}\right) \\ $$$${p}=\underset{{r}=\mathrm{2}} {\overset{\mathrm{12}} {\sum}}{C}_{{r}} ^{\mathrm{12}} ×\mathrm{0}.\mathrm{3}^{{r}} ×\mathrm{0}.\mathrm{7}^{\mathrm{12}−{r}} =\mathrm{0}.\mathrm{915} \\ $$$$\left({b}\right) \\ $$$${p}={C}_{\mathrm{6}} ^{\mathrm{12}} ×\mathrm{0}.\mathrm{3}^{\mathrm{6}} ×\mathrm{0}.\mathrm{7}^{\mathrm{6}} =\mathrm{0}.\mathrm{079} \\ $$$$\left({c}\right) \\ $$$${p}=\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}} {\sum}}{C}_{{r}} ^{\mathrm{12}} ×\mathrm{0}.\mathrm{3}^{{r}} ×\mathrm{0}.\mathrm{7}^{\mathrm{12}−{r}} =\mathrm{0}.\mathrm{253} \\ $$

Commented by Tawa11 last updated on 09/Jul/24

$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}. \\ $$

Commented by Tawa11 last updated on 10/Jul/24

Sir please, any luck for me on Q209430, thanks sir.

$$\mathrm{Sir}\:\mathrm{please},\:\mathrm{any}\:\mathrm{luck}\:\mathrm{for}\:\mathrm{me}\:\mathrm{on}\:\mathrm{Q209430},\:\mathrm{thanks}\:\mathrm{sir}. \\ $$

Commented by mr W last updated on 10/Jul/24

$${i}\:{have}\:{given}\:{the}\:{answers}.\:{but}\:{i}\:{don}'{t} \\ $$$${think}\:{it}\:{may}\:{really}\:{help}\:{you}.\: \\ $$

Commented by Tawa11 last updated on 10/Jul/24

Though, I understand the workings sir, But I don′t understand the concept.

$$\mathrm{Though},\:\mathrm{I}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{workings}\:\mathrm{sir}, \\ $$$$\mathrm{But}\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{concept}. \\ $$

Commented by mr W last updated on 11/Jul/24

$${just}\:{filling}\:{in}\:{formula}\:{without} \\ $$$${understanding}\:{makes}\:{little}\:{sense}. \\ $$$${the}\:{theme}\:{is}\:{much}\:{more}\:{complex} \\ $$$${than}\:{the}\:{simple}\:{motion}\:{of}\:{a} \\ $$$${projectile}\:{in}\:{vertical}\:{direction}. \\ $$

Commented by Tawa11 last updated on 11/Jul/24

Wow. Tell me topic I can learn this more sir, or link or book. I will study it.

$$\mathrm{Wow}. \\ $$$$\mathrm{Tell}\:\mathrm{me}\:\mathrm{topic}\:\mathrm{I}\:\mathrm{can}\:\mathrm{learn}\:\mathrm{this}\:\mathrm{more} \\ $$$$\mathrm{sir},\:\mathrm{or}\:\mathrm{link}\:\mathrm{or}\:\mathrm{book}.\:\mathrm{I}\:\mathrm{will}\:\mathrm{study}\:\mathrm{it}. \\ $$

Commented by mr W last updated on 11/Jul/24

i don′t mean this question, i mean Q209430. it′s about forced damped harmonic oscillator

$${i}\:{don}'{t}\:{mean}\:{this}\:{question},\:{i}\:{mean} \\ $$$${Q}\mathrm{209430}.\:{it}'{s}\:{about}\: \\ $$forced damped harmonic oscillator

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