Unformatted text preview: WW Fur :vemsA and a, the mummy mm A and a bum occur equals,
Pu m5) = P(B) x rum) Apply"; the «mama! mummy funnula to P(EA), we alsa see um,
P(A and a) = Pu) x mm) m m a mums «and. a pm" mzde (nuns on he ﬁrst serve 44% am»: xime and anlv 2% on his second serves. Find the mohahllllvtha he with: I douhk flu".
in “man =c‘eoen , p H
0.01
r
03'
a“ 5 rs (guano 95) :4: m:
use
5‘ 5 as:
mentor: P(I'F) = 0.0068
£811.: Sunpﬂnl am. or whom nplaumem There is : Donlalnel in mm of you whch mnuins 25 pens. Oul af these 15 pens, 10 unhem wrlle well. And 5 at them
an defective. Vuu will he asked to select two of them. Find the vruhabilltv that both of them are defective cm I: wnn replxement 1/5 D an 1/25
D
Ils'
£IS 6 DG 4125
mp)
1/5 n so 4115
1/5
6
”S G 66 “/15
‘1 , a _ A
m
V
/ , N
an; r\
"IL, Case ll: Without replacement om  115 D on u/sm/s;  use
5/25  1/5 °
IONASIS 5 D6 lI/5H5/631/E
salon)
5/2: an u/susml  us
20/15  4/5 a
“I" 5 as u/sms/m  um
I ' I p Evenxs A and a are Independent, Mum) = PM), or equivalently, il P(BA) = my) lleimeruhhem holds, mum:
olhev does mo, and also, P(A and a) = PM) x P(B). Nate: Vuu can check for independence 0' two events A and B by checking one o! the knowing three (auditions.  ls pals; = ppm
 ls mm) = P(8)7
 ls P(A and a) = Pu) x my)? Ex ll: 5.45: For a family with Mo children, lel A dame (ﬁrst child is ’emale] and let C dennte (ham children Ire
lemale). Find whether A and E are independent 1,; v r: 1/.
r
2/1
x11 M m In
1/ 1 r M: 1/;
1/1
M
”I M MM 1/. fund whemer A and C are independent
1 P(A) = ;p(c) = P(FF) = z 4‘ P(A and c) = P(FF) = E; P(A) x P(C) = x NI.
+1
ml» Therefore, PM and c) s PM) x P(C) Hence, Am c ave no! independent, ...
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 Spring '08
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 Statistics

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