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lec0328 - CS 173 Discrete Mathematical Structures Cinda...

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CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebel Center, rm 2213 Office Hours: BY APPOINTMENT

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Cs173 - Spring 2004 CS 173 Announcements Homework 9 available.  Due 04/02, 8a. Exam 2, Apr 4, 7-9p, Loomis 141. Email Cinda with conflicts. Today’s lecture covers material from Rosen, sections 5.2-5.3.
Cs173 - Spring 2004 CS 173 Probability Which is more likely: a) Rolling an 8 when 2 dice are rolled? b) Rolling an 8 when 3 dice are rolled? c) No clue.

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Cs173 - Spring 2004 CS 173 Probability What is the probability of a total of 8 when 2 dice are rolled? What is the size of the sample space? 36 How many rolls satisfy our condition of interest? 5 So the probability is 5/36.
Cs173 - Spring 2004 CS 173 Probability What is the probability of a total of 8 when 3 dice are rolled? What is the size of the sample space? 216 How many rolls satisfy our condition of interest? C(7,2) So the probability is 21/216.

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Cs173 - Spring 2004 CS 173 Conditional Probability Let E and F be events with Pr(F) > 0.  The conditional probability  of E given F, denoted by Pr(E|F) is defined to be: Pr(E|F) = Pr(E F)/Pr(F). F E
Cs173 - Spring 2004 CS 173 Conditional Probability Pr(E|F) = Pr(E F)/Pr(F). A bit string of length 4 is generated at random so that each of the 16  bit strings is equally likely.  What is the probability that it contains  at least two consecutive 0s, given that its first bit is a 0? Pr(F) = 1/2 Pr(E F)? 0000  0001 0010  0011  0100  Pr(E F) = 5/16 Pr(E|F) = 5/8

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Cs173 - Spring 2004 CS 173 Independence The events E and F are independent if and only if Pr(E F) = Pr(E)  x Pr(F). Let E be the event that a family of n children has children of both sexes. Lef F be the event that a family of n children has at most one boy. Are E and F independent if  n = 2?  No
Cs173 - Spring 2004 CS 173 Independence The events E and F are independent if and only if Pr(E F) = Pr(E)  x Pr(F). Let E be the event that a family of n children has children of both sexes. Lef F be the event that a family of n children has at most one boy. Are E and F independent if  n = 3?  Yes

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Cs173 - Spring 2004 CS 173 Independence The events E and F are independent if and only if Pr(E F) = Pr(E)  x Pr(F).
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lec0328 - CS 173 Discrete Mathematical Structures Cinda...

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