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

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Q.
Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiable 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 [2025]

1 $\frac{18}{25}$

2 $\frac{14}{25}$

3 $\frac{28}{75}$

4 $\frac{26}{75}$

Ans.
(3)

Given, x denote the number of defective oranges, out of two. So, the probability distribution is given below as:

$x_{i}$ x = 0 x = 1 x = 2

$P (x = x_{i})$ $\frac{{}^{7}C_{2}}{{}^{10}C_{2}} = \frac{7}{15}$ $\frac{{}^{7}C_{1} \times {}^{3}C_{1}}{{}^{10}C_{2}} = \frac{7}{15}$ $\frac{{}^{3}C_{2}}{{}^{10}C_{2}} = \frac{1}{15}$

Mean $(μ) = \sum_{i = 0}^{2} x_{i} p_{i} = \frac{9}{15} = \frac{3}{5}$

and $σ^{2} = \sum_{i = 0}^{2} p_{i} x_{i}^{2} - μ^{2} = \frac{11}{15} - {(\frac{3}{5})}^{2} = \frac{28}{75}$

Solution

Q.
Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiable 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 [2025]

1 $\frac{18}{25}$

2 $\frac{14}{25}$

3 $\frac{28}{75}$

4 $\frac{26}{75}$

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$x_{i}$	x = 0	x = 1	x = 2
$P (x = x_{i})$	$\frac{{}^{7}C_{2}}{{}^{10}C_{2}} = \frac{7}{15}$	$\frac{{}^{7}C_{1} \times {}^{3}C_{1}}{{}^{10}C_{2}} = \frac{7}{15}$	$\frac{{}^{3}C_{2}}{{}^{10}C_{2}} = \frac{1}{15}$

Solution

Q. Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiable 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 [2025]

1 1825

2 1425

3 2875

4 2675

Ans. (3) Given, x denote the number of defective oranges, out of two. So, the probability distribution is given below as: xi x = 0 x = 1 x = 2 P(x=xi) C27C210=715 C17×C13C210=715 C23C210=115 Mean (μ)=∑i=02xipi=915=35 and σ2=∑i=02pixi2–μ2=1115–(35)2=2875

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Q.
Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiable 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 [2025]

1 $\frac{18}{25}$

2 $\frac{14}{25}$

3 $\frac{28}{75}$

4 $\frac{26}{75}$