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 We have 2 choices for each bit and a sequence of 8 bits. Then the number of possible results is (2)8 

 = 256.

(b) The simplest form of the Multiplication Rule for probabilities is as follows: If the events are independent, then the occurrence of one event does not affect the  probability of occurrence of another event. In that case the probability of occur- rence of more than one event together is the product of the probabilities of the separate events. (This is consistent with the basic idea of counting stated above.)  

If A and B are two separate events that are independent of one another, the probability of occurrence of both A and B together is given by:  

Pr [A ∩ B] = Pr [A] × Pr [B]

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