Re: can Mathematica be useful for this?

*To*: mathgroup at smc.vnet.net*Subject*: [mg56595] Re: can Mathematica be useful for this?*From*: Maxim <ab_def at prontomail.com>*Date*: Fri, 29 Apr 2005 03:22:07 -0400 (EDT)*References*: <d4kks5$eck$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Tue, 26 Apr 2005 05:51:01 +0000 (UTC), <pedrito6 at softhome.net> wrote: > Hi there! > > I need to check the answer of many probability problems. > Most of them are quite simple but calculating them by hand is tedious. > > They are like this: > "It's necessary to choose a person for a mission overseas. If you choose > him randomly the probability that he speaks a foreign languague is: > S=Spanish; F=French; G=German > P(S)=0.33; P(F)=0,26; P(G)=0.2; > P(S and F)=0.15; P(F and G)=0.05; P(S and G)=0.1 > P(S and F and G)=0.02 > > -What is the probability that he just speaks one foreign language? > -What is the probability that he doesn't speak any?" > > Could be Mathematica useful for solving this kind of problems? > > Thanks for your help! > You can use the inclusion-exclusion principle: In[1]:= SetAttributes[p, Orderless] p[] = 1.; p[F] = .26; p[G] = .2; p[S] = .33; p[F, G] = .05; p[F, S] = .15; p[G, S] = .1; p[F, G, S] = .02; In[10]:= <<discretemath` With[{n = 3}, Table[Sum[(-1)^(k - r)*Binomial[k, r]* Total[p@@@ KSubsets[{F, G, S}, k]], {k, r, n}], {r, 0, n}] ] Out[11]= {0.49, 0.25, 0.24, 0.02} This is the list of probabilities that the person knows exactly 0, 1, 2, 3 languages respectively. Maxim Rytin m.r at inbox.ru