Midterm Exam 1 Solutions
CS70 Blum/Wagner, 9 March 2001
This is a CLOSED BOOK examination. One page of notes is permitted. Calculators are permitted. Do all your
work on the pages of this examination. Give reasons for all your answers.
Problem 1 (Short answer grabbag)
[10 Points]
For parts (a)(c), justify your answer briefly.
(a) [2 Points] True or False: (P => Q) => (Q => P) always holds, for all propositions P, Q.
False. Counter example: P=False, Q=True. This is a converse error.
(b) [3 Points] True or False: ((P v Q) => Q) => (Q => (P v Q)) always holds, for all propositions P, Q.
True. (Q => (P v Q)) = True for all P,Q, and (anything => True) is true.
(Don't be fooled into thinking this is another converse error. It's not.)
(Common error: Not realizing that (False => False) is True.)
(c) [3 Points] Recall that two sest S,T are said to be
disjoint
if
= Ø. Can two events A and B be
simultaneously independent and disjoint?
Yes. An example: If A = Ø, then A isect B = Ø and Pr[A]=0.
So, Pr[A isect B] = 0 = 0 × Pr[B] = Pr[A]Pr[B], and A,B are independent and disjoint.
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 Spring '08
 PAPADIMITROU
 Probability theory, #, uniform probability distribution, random variable Note

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