Question

A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.

Answer 1

Let X denote the number of white balls when 2 balls are drawn from the bag.

X follows a distribution with values 0,1 or 2.


$$\begin{gathered} P(X=0)=\mathit{}P(\mathrm{All}\mathrm{balls}\mathrm{non}-\mathrm{white})=\frac{{}^{\mathit{7}}C_2}{{}^{9}C_2}=\frac{42}{72}=\frac{21}{36} \\ P(X=1)=P\hspace{0.17em}(\mathrm{Ist}\hspace{0.17em}\mathrm{ball}\mathrm{white}\mathrm{and}\mathrm{IInd}\mathrm{ball}\mathrm{non}-\mathrm{white})\hspace{0.17em} \\ =\frac{{}^{7}C_1{}^{2}C_1}{{}^9\mathrm{C}_2}=\frac{14}{36} \\ P(X=2)=P(\mathrm{Both}\mathrm{balls}\mathrm{white})=\frac{{}^{2}C_2}{{}^{9}C_2}=\frac{1}{36} \\ \mathrm{It}\mathrm{can}\mathrm{be}\mathrm{shown}\mathrm{in}\mathrm{tabular}\mathrm{form}\mathrm{as}\mathrm{follows}. \\ X012 \\ P\left(X\right)\frac{21}{36}\frac{14}{36}\frac{1}{36} \end{gathered}$$