an urn contains 7 white , 5 black and 3 red balls . two balls are drawn at rendom. find the probability that
1 both the balls are red
2. one ball is red and the other black
3. one ball is white

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} 1\mathrm{st} \mathrm{part} \\ \mathrm{Probability} \mathrm{that} \mathrm{both} \mathrm{the} \mathrm{balls} \mathrm{are} \mathrm{white}=\frac{{}^3\mathrm{C}_2}{{}^{15}\mathrm{C}_2}=\frac{3}{105}=0.028 \left(\mathrm{Answer}\right) \\ 2\mathrm{nd} \mathrm{part} \\ \mathrm{Probability} \mathrm{that} \mathrm{one} \mathrm{ball} \mathrm{is} \mathrm{red} \mathrm{and} \mathrm{other} \mathrm{one} \mathrm{is} \mathrm{black}=\frac{3\times 5}{{}^{15}\mathrm{C}_2}=\frac{15}{107}=0.14 \left(\mathrm{Answer}\right) \\ 3\mathrm{rd} \mathrm{part} \\ \mathrm{Probability} \mathrm{that} \mathrm{one} \mathrm{ball} \mathrm{is} \mathrm{white}\left(\mathrm{P}\right)=1-\mathrm{probability} \mathrm{that} \mathrm{none} \mathrm{of} \mathrm{ball} \mathrm{is} \mathrm{white}\left({\mathrm{P}}_1\right) \\ \mathrm{So} \\ {\mathrm{P}}_1=\frac{{}^8\mathrm{C}_2}{{}^{15}\mathrm{C}_2}=\frac{28}{105}=0.266 \\ \mathrm{So} \mathrm{P}=1-0.266=0.734 \left(\mathrm{Answer}\right) \end{gathered}$$

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