Mathematics - Probability Question with Solution | TestHub

Event ${\mathrm{A}}_1=$ urn contains 5 white balls Event $\mathrm{A}=$ Event ${\mathrm{A}}_2=$ urn contains 4 white balls Drawing two white balls when two Event $A_3=$ urn contains 3 white balls balls are drawn from five balls Event ${\mathrm{A}}_4=$ urn contains 2 white balls

$$\begin{array}{rlrlr}& \mathrm{P}\left(\frac{{\mathrm{A}}_1}{\mathrm{A}}\right)=\frac{\mathrm{P}\left({\mathrm{A}}_1\right)\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_1}\right)}{\mathrm{P}\left({\mathrm{A}}_1\right)\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_1}\right)+\mathrm{P}\left({\mathrm{A}}_2\right)\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_2}\right)+\mathrm{P}\left({\mathrm{A}}_3\right)\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_3}\right)+\mathrm{P}\left({\mathrm{A}}_4\right)\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_4}\right)}& \mathrm{P}\left({\mathrm{A}}_1\right)=\mathrm{P}\left({\mathrm{A}}_2\right)=\mathrm{P}\left({\mathrm{A}}_3\right)=\mathrm{P}\left({\mathrm{A}}_4\right)=\frac{1}{4}& \mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_1}\right)=1,\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_2}\right)=\frac{{}^4{\mathrm{C}}_2}{{}^5{\mathrm{C}}_2},\mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_3}\right)=\frac{{}^3{\mathrm{C}}_2}{{}^5{\mathrm{C}}_2}& \mathrm{P}\left(\frac{\mathrm{A}}{{\mathrm{A}}_4}\right)=\frac{{}^2{\mathrm{C}}_2}{{}^5{\mathrm{C}}_2}\end{array}$$