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Homework 4 - S is in exactly two of the three sets A B C OJ...

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: September 14, 2010 Math 351 - Homework 4 Due in class on Thursday. 1. Three sets A, B, C which lie in a sample space S satisfy the following: P(A) .3 P(B) = .33 P(C) .17 P(AB) .08 P(AC) = .07 P(BC) = .1 P(A C BCC C ) .4 (a) Use De :vlorgan's rule to find P(A U B U C). ~t ::: PCA~~C.c/:. f'(tJ v/J vc );":. /- //A-u/J cJ C} 8 tP;,/;u/,jv C):::-. 6 (b) Use the inclusion-exclusion principle to find P(ABC). I'I4u/Juc/~ .A14)+I'I/3) f jJ('c)-L/d1~Jt-;tJt7f c/~CJjr I't»d c} "1 0.":: t) f·.I3 '1'./7 ) -( 0 e -f 07"'. d r [f1/(,f /l C).,. .S-S-" ,fi'C4,11. /. jJ('II-8 C)=- c- b '-"rr ~ · 0S (c) Make a three-set Venn diagram and fill in all of the eight probabilities. (d) Use your Venn diagram to decide what is the probability that a randomly chosen object of
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Unformatted text preview: S is in exactly two of the three sets A, B, C . .. OJ ~ ,. 0 2... .'1-,. OJ::' • / 2. A forest contains 25 elk, of which 15 are captured. tagged and then released. A certain time later 10 of the elk arc captured. What is the probability that either 5 or 6 of them arc I(r I q-to/ r 1)+ ~(6 / q~c/ ~ ~ / -_ (;1 -(r;)-f ~:t~aJ ~E:0 ... ¢!) f;) 3. Ten people, designated as A, C, D. E. F, G, II. I, J, are randomly arranged in chairs in a straight line. What is the probability that A, B, and C occupy three chairs that are next to each other (but in no specified order)? / I I_/' A/}(; {v-t'WI. n /001/ "T nl 'I ] ? {] ./-7 1)(/,,,,. .,1-<-tie floc;{ 0-1<1 f6 ? o/i(e. .J Jlj6l-~ I-iJ fil!jj leV...
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