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Re: can Mathematica be useful for this?

Here is another approach:

For each language, let's use 1 to indicate that the person can speaks
it and 0 that he cannot. So a binary vector of length 3 describes what
languages the person speaks. For example, {S=1, F=0, G=0}, or {1, 0, 0}
means that he can speak Spanish only. The probably corresponding to
such vector is denoted by p[S,F,G] (lower case p).  All the
probabilities listed in the problem are functions of p[S,F,G] (all 8 of
them). For example, probability that the person can speak S and F, P[S
and F]=p[1,1,0]+p[1,1,1] (note the difference between upper case P and
lower case p), etc.

We need to write P in terms of p and solve for p which is the answer we

The probabilities listed in the problem are



Now write each of them in terms of p:





The equation to be solved:


Plus the condition that all p's sum to 1:

Solve for p:

sol=Solve[Append[eqn, Total[unknown]==1],unknown]


Hence the probability that the person doesn't speak any is
p[0,0,0]=73/150, and the probability that he speaks one only is



K. Zhang

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