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Question Number 176056 by otchereabdullai@gmail.com last updated on 11/Sep/22

$$\mathrm{Three}\mathrm{bags}\mathrm{labelled}\mathrm{R},\mathrm{B}\mathrm{and}\mathrm{W}$$$$\mathrm{cotains}\mathrm{Red},\mathrm{Blue}\mathrm{and}\mathrm{White}\mathrm{balls}$$$$\mathrm{respectively}\mathrm{of}\mathrm{equal}\mathrm{sizes},\mathrm{the}\mathrm{ratio}$$$$\mathrm{of}\mathrm{the}\mathrm{balls}\mathrm{in}\mathrm{the}\mathrm{bag}\mathrm{are}\mathrm{R}:\mathrm{B}=2:3$$$$\mathrm{and}\mathrm{B}:\mathrm{W}=4:5.\mathrm{All}\mathrm{the}\mathrm{balls}\mathrm{are}$$$$\mathrm{removed}\mathrm{into}\mathrm{a}\mathrm{big}\mathrm{bag}\mathrm{and}\mathrm{properly}$$$$\mathrm{mixed}\mathrm{together}.\mathrm{If}\mathrm{two}\mathrm{balls}\mathrm{are}\mathrm{picked}$$$$\mathrm{at}\mathrm{random}\mathrm{one}\mathrm{after}\mathrm{the}\mathrm{other}\mathrm{with}$$$$\mathrm{replacement},\mathrm{find}\mathrm{the}\mathrm{probability}\mathrm{of}$$$$\mathrm{picking}$$$$\mathrm{a})\mathrm{white}\mathrm{ball}\mathrm{and}\mathrm{a}\mathrm{blue}$$$$\mathrm{b}).\mathrm{A}\mathrm{blue}\mathrm{ball}\mathrm{first}\mathrm{and}\mathrm{then}\mathrm{red}\mathrm{ball}$$$$$$

Answered by mr W last updated on 11/Sep/22

$$\frac{R}{B}=\frac{2}{3}$$$$\frac{B}{W}=\frac{4}{5}$$$$R+B+W=1$$$$\frac{2B}{3}+B+\frac{5B}{4}=1$$$$\Rightarrow B=\frac{12}{35}$$$$\Rightarrow R=\frac{2}{3}\times \frac{12}{35}=\frac{8}{35}$$$$\Rightarrow W=\frac{5}{4}\times \frac{12}{35}=\frac{15}{35}$$$$i.e.whenpickingaballfromthebig$$$$bag,theprobabilitythat{it}^{\prime }saredball$$$$is\frac{8}{35},theprobabilitythat{it}^{\prime }sablueball$$$$is\frac{12}{35},theprobabilitythat{it}^{\prime }sawhiteball$$$$is\frac{15}{35}.$$$$a)$$$$firstwhiteandsecondblueor$$$$firstblueandsecondwhite$$$$p=\frac{15}{35}\times \frac{12}{35}+\frac{12}{35}\times \frac{15}{35}=\frac{72}{245}=0.294$$$$b)$$$$firstblueandsecondred$$$$p=\frac{12}{35}\times \frac{8}{35}=\frac{96}{1225}=0.078$$

Commented by otchereabdullai@gmail.com last updated on 11/Sep/22

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{prof}\mathrm{W}$$

Commented by peter frank last updated on 11/Sep/22

$$\mathrm{thank}\mathrm{you}$$

Commented by Tawa11 last updated on 15/Sep/22

$$\mathrm{Great}\mathrm{sir}$$

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