Probability Let A, B and C be Boolean variables denoting three independent events with P(A=1) =...

Probability

Let A, B and C be Boolean variables denoting three independent events with P(A=1) = 0.7, P(B=1) = 0.3, and P(C=1) = 0.1. Let D be the event that at least one of A and B occurs, i.e., D = A OR B. Let E be the event that at least one of B and C occurs, i.e., E = B OR C. Let F be the event that exactly one of A and B occurs, i.e., F = A XOR B.

(a) (4 pts) Express F as a set of clauses (i.e., as a conjunction of disjunctions) involving A and B.

(b) (9 pts) Suppose that A and E are true. What is the probability that B is true? Show your work.

(c) (9 pts) Suppose that D and E are true. What is the probability that A is true? Show your work.

Expert Solution

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orchestra answered 1 year ago

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