Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denote the number of defective oranges, then the variance of $x$ is

Question

Aicharya · Accepted Answer

There are 3 bad oranges and 7 good oranges. $\therefore \quad X=$ number of bad oranges drawn.

$\therefore$ Variance
$\begin{aligned}
& =0^2 \cdot \frac{{ }^7 C_2}{{ }^{10} C_2}+1^2 \cdot\left(\frac{3 \times 7}{{ }^{10} C_2}\right)+2^2\left(\frac{3}{{ }^{10} C_2}\right) \\ & \quad-\left(0+1 \cdot \frac{3 \times 7}{{ }^{10} C_2}+2 \cdot \frac{3}{{ }^{10} C_2}\right)^2 \\ & =\frac{28}{75}
\end{aligned}$ /

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible…

Solution