Probability of a boolean formula which use only xor and and operations

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Can I obtain the probability formula from a boolean formula only translating and operator by the multiplication operator; and the xor operator by the sum operator?

For example Pr[(a and b) xor c = 1] = Pr[a=1]*Pr[b=1]+Pr[c=1]?

EDIT

In case no, are there any general rules to get the probability expression using the boolean formula? (Suppose events totally independent)