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February 28th, 2012, 08:56 PM   #1
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Probability and Expectation of Logical Propositions

Given seven propositions of the form in which the variables in each proposition are all different(although variables may be repeated throughout the other seven propositions) and may also be negated.

a. what is the probability that a single proposition is true?
my attempt:
A proposition is true if it has at least one true value. The number of propositions with at least one true = total true/false outcomes - number of propositions with no true values =
Pr[proposition is true] =

b. What is the expected number of true propositions
random variable denoting the number of True propositions
random variable indicating whether the proposition is 1: true or 0: false

Am I on the right track or am I completely wrong?
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