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Unformatted text preview: s different.
i. What is Pr[C]?
Solution: 1 . z can be any value other than zero.
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CS 70, Fall 2013, Midterm #2 1 Name: SID:
Alternate interpretation:
3x−1 . 6
49 . Let x take on any nonzero value (6 possibilities) and y equal ii. What is Pr[A ∩ B]?
1
Solution: 36 . Both x and y are equal to 3 with probability ( 1 )2 .
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1
Alternate interpretation: 49 . Both x and y are equal to 3 with probability ( 1 )2 .
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iii. What is Pr[A ∩ C]?
1
Solution: 36 .This means that x = 3 and y = 1, which occurs with probability ( 1 )2 .
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1
Alternate interpretation: 49 .This means that x = 3 and y = 1, which occurs with probability ( 1 )2 .
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iv. What is Pr[B ∩ C]?
1
Solution: 36 . This means that y = 3 and x = 1, which occurs with probability ( 1 )2 .
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1
Alternate interpretation: 49 . This means that y = 3 and x = 1, which occurs with probability ( 1 )2 .
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v. Are A,B,C pairwise independent?
Yes
No
Are A,B,C pairwise independent? Alternate interpretation: Yes No (g) (5 points) Suppose A and B are disjoint events such that P[A] = 0 and P[B] = 0. i. What is Pr[A ∩ B]?
Solution: 0. The events are disjoint so their intersection is empty (it contains no sample
points). ii. Can A and B be independent?
Yes
No
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