Set probability

Let the set X={x1, x2, x3}, if P({x1})=.4 and P({x1,x3})= .5 find probability of P(power set of X) =? ....P= probability.


Attempt. Since probability of a set is the membership function m(x1) for instance, then I thought that probability of the power set will the Sum of probability of all of the sets.
That is P(power set X)= .4+.5+ bunch of 0= .9.
But I am really not sure. if anyone can help it wil be so awesome! I am just confused by this. I'll have a fuzzy set theory like problems to do.

Is P{x1 or x2 or x3}=1? In other words, is the occurrence of at least one of the three elements mandatory?

This is odd, to me. If X is the sample space, it is unusual to assign a probability to the power set. Probabilities are assigned to subsets of X - elements of the power set (not necessarily all of them though) - and not usually to the power set itself. More explicitly, the power set of the sample space isn't usually in the domain of the probability function.

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Originally Posted by Sambit

Is P{x1 or x2 or x3}=1? In other words, is the occurrence of at least one of the three elements mandatory?

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there is no mendatory probbility on x1, x2, or 3.
So no occurence. Is mandatory, but now that U guys r talking I should recall that P(X) must eqal 1so my attemt definetely weak.

To theodds.
I think the Way u tacle the problem, make sense. so the qstion asked was " determine the probability measure on power set Of X, but I thought this stemnt is eqivalent to P({power set of X}).
So reconsidering the question with same conditions, find probability measure on power set of X. I hope this makes more sense now.

Quote:

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Originally Posted by karlito03

there is no mendatory probbility on x1, x2, or 3.
So no occurence. Is mandatory, but now that U guys r talking I should recall that P(X) must eqal 1so my attemt definetely weak.

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After reading the above, here is my guess.
Because elementary events are disjoint, .
Thus that implies that .
Can you find

.4,.5,.1