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Chapter 5 Notes (6)

# Chapter 5 Notes (6) - WW Fur:vemsA and a the mummy mm A and...

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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(E|A), 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 wh|ch 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 ° IONA-SIS 5 D6 lI/5H5/63-1/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(B|A) = 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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