Mathematics - Probability Question with Solution | TestHub

${\mathrm{E}}_1$ : Event denotes spade is missing 

$P\left(E_1\right)=\frac{1}{4};P\left({\overline{E}}_1\right)=\frac{3}{4}$

$A$ : Event drawn two cards are spade 

$P\left(\frac{A}{E_1}\right)=\left(\frac{{}^{12}\mathrm{C}_2}{{}^{51}\mathrm{C}_2}\right), P\left(\frac{A}{\overline{E_1}}\right)=\left(\frac{{}^{13}\mathrm{C}_2}{{}^{51}\mathrm{C}_2}\right)$

$P\left(\frac{E_1}{A}\right)=\frac{\frac{3}{4}\times \left(\frac{{}^{13}\mathrm{C}_2}{{}^{51}\mathrm{C}_2}\right)}{\frac{1}{4}\times \left(\frac{{}^{12}\mathrm{C}_2}{{}^{51}\mathrm{C}_2}\right)+\frac{3}{4}\times \left(\frac{{}^{13}\mathrm{C}_2}{{}^{51}\mathrm{C}_2}\right)}$$=\frac{39}{50}$