Answer to Question #239424 in Statistics and Probability for Tawki

Question

Before the distribution of gadgets, the teacher will test two tablets. Use D for defective tablet, Nfor
non-defective tablet.
Let X be the random variable representing the number of defective tablet that will occur.
Complete the table below and find the values of random variable X.

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} \text{Possible } & \text{Values of the } \\ \text{Outcomes} & \text{Random Variable} \ L\\ \hline LL & 2 \\ LY & 1 \\ YL & 1\\ YY & 0 \end{array}$$ $$P(L=0)=\dfrac{\dbinom{3}{0}\dbinom{10-3}{2-0}}{\dbinom{10}{2}}=\dfrac{21}{45}=\dfrac{7}{15}$$ $$P(L=1)=\dfrac{\dbinom{3}{1}\dbinom{10-3}{2-1}}{\dbinom{10}{2}}=\dfrac{21}{45}=\dfrac{7}{15}$$ $$P(L=2)=\dfrac{\dbinom{3}{2}\dbinom{10-3}{2-2}}{\dbinom{10}{2}}=\dfrac{3}{45}=\dfrac{1}{15}$$ $$\def\arraystretch{1.5} \begin{array}{c:c} l & 0 & 1 & 2 \\ \hdashline \\ P(L=l) & \dfrac{7}{15} & \dfrac{7}{15} & \dfrac{1}{15} \end{array}$$