An urn contains 4 white and 3 red balls Let X be the number of red balls in a - Maths - Probability

Question

An urn contains 4 white and 3 red balls Let X be the number of red
balls in a random draw of three balls Find the mean
and variance of X

Neha Sethi · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5aa95a7e0562f%20png"
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Now, Mean EX=p1x1+p2x2+p3x3+p4x4=0×435+1×1835+2×1235+3×135=0+1835+2435+335=97Variance VX :

xi
pi=PX=xi
pixi
pixi2

0
435
0
0

1
1835
1835

1835

2
1235
2435
4835

3
135
335
935

=∑pixi=97
=∑pixi2=157

VarX=∑pixi2-∑pixi2=157-972=157-8149=2449
Regards

$x_{i}$	$p_{i} = P (X = x_{i})$	$p_{i} x_{i}$	$p_{i} {x_{i}}^{2}$
0	$\frac{4}{35}$	0	0
1	$\frac{18}{35}$	$\frac{18}{35}$	$\frac{18}{35}$
2	$\frac{12}{35}$	$\frac{24}{35}$	$\frac{48}{35}$
3	$\frac{1}{35}$	$\frac{3}{35}$	$\frac{9}{35}$
		$= \sum_{}^{} p_{i} x_{i} = \frac{9}{7}$	$= \sum_{}^{} p_{i} {x_{i}}^{2} = \frac{15}{7}$

An urn contains 4 white and 3 red balls. Let X be the number of red balls in a random draw of three balls. Find the mean and variance of X.