An urn contains 5 red and 2 black balls. Two balls are randomly d… - Vidyadip

Question

An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls drawn. What are the possible values of X? Is X a random variable? If yes, find the mean and variance of X.

✓

Answer

Possible values of x are 0, 1, 2 and x is a random variable:

$\text{x:}$	$\text{P(x)}$	$\text{x P(x)}$	$\text{x}^{2} \text{P(x)}$
0	$\frac{^2{\text{C}_{0}}\times^5{\text{C}_{2}}}{^7{\text{C}_{2}}} = \frac{20}{42}$	0	0	$\text{For P (x)}$
1	$\frac{^2{\text{C}_{1}}\times^5{\text{C}_{1}}}{^7{\text{C}_{2}}} = \frac{20}{42}$	$\frac{20}{40}$	$\frac{20}{42}$	$\text{For x P (x)}$
2	$\frac{^2{\text{C}_{2}}\times^5{\text{C}_{0}}}{^7{\text{C}_{2}}} = \frac{2}{42}$	$\frac{4}{42}$	$\frac{8}{42}$	$\text{For x}^{2}\text{ P (x)}$

$\sum \text{x P(x)} = \frac{24}{42}; \sum \text{x}^{2} \text{ P(x)} = \frac{28}{42}$ $\text{Mean} = \sum \text{x P(x)} = \frac{4}{7}; \text{variance} = \sum \text{x}^{2} \text{P(x)} - \bigg[\sum \text{x P (x)}\bigg]^{2}$ $\text{Variance} = \frac{50}{147} =\frac{2}{3}- \frac{16}{49} = \frac{50}{147} $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\text{If}\ \text{x}=\text{a}(2\theta-\sin2\theta)\ \text{and}\ \text{y}=\text{a}(1-\cos2\theta),\ \text{find}\ \frac{\text{dy}}{\text{dx}}\ \text{when}\ \theta=\frac{\pi}{3}.$

Two tailors, A and B earn Rs. 15 and Rs. 20 per day respectively. A can stitch 6 shirts and 4 pants while B can stitch 10 shirts and 4 pants per day. How many days shall each work if it is desired to produce (at least) 60 shirts and 32 pants at a minimum labour cost?

A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below:

Food	Vitamin A	Vitamin B	Vitamin C
X	1	2	3
Y	2	2	1

One kg of food X costs Rs. 16 and one kg of food Y costs Rs. 20. Find the least cost of the mixture which will produce the required diet?

Differentiate the following functions with respect to x:
$\text{x}^{\frac{1}{\text{x}}}$

Show that the vector $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ is equally inclined to the coordinate axes.

Differentiate $\tan^{-1} \bigg(\frac{\sqrt{1 + x^{2} - 1}}{x}\bigg)$ w.r.t. $\sin^{-1} \frac{2x}{1 + x^{2}}, \text{ if } x \in (-1, 1)$

Differentiate $\sin^{-1}\Big\{\frac{2^{\text{x}+1}\times3^\text{x}}{1+(36)^\text{x}}\Big\}$ with respect to x:

If $y^3+3 a x^2+x^3=0$ then prove that:$
\frac{d^2 y}{d x^2}+\frac{2 a^2 x^2}{y^5}=0
$

If $\vec{\text{a}}=\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}},\vec{\text{b}}=\text{b}_1\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}$ and $\vec{\text{c}}=\text{c}_1\hat{\text{i}}+\text{c}_2\hat{\text{j}}+\text{c}_3\hat{\text{k}},$ then verify that $\vec{\text{a}}\times\big(\vec{\text{b}}+\vec{\text{c}}\big)=\vec{\text{a}}\times\vec{\text{b}}+\vec{\text{a}}\times\vec{\text{c}}.$

$\int\frac{\text{x}}{\sqrt{\text{x}+\text{a}}-\sqrt{\text{x}+\text{b}}}\text{dx}$