IE111_Exam1a_solutions

IE111_Exam1a_solutions - IE 111 9:00 Section Exam 1 Fall...

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IE 111 Solutions 9:00 Section Exam 1 Fall 2009 Question 1 Consider the events shown in the Venn diagram above: Suppose P(A)=0.4 P(B)=0.2 P(C)=0.3 P(D)=0.7 P(A|B)=0.1. Suppose also that B and D are independent. (Please compute a final probability (a number) for each part). a) Find P(B|C) 0, since if C happens, then B cannot happen b) Find P(C ′∩ D) Since C is included in D, this is P(D)-P(C)=0.4. c) Find P(A ′∩ B ′∩ D) =P(D)-P(B D)=0.7-P(B)P(D)=0.56 (B and D are independent, so the probabilities multiply) d) Find P(C D) =P(D)=0.7 e) Find P(A B) P(A B)=P(A)+P(B)-P(A B)=0.4+0.2-P(A|B)P(B)=0.6-0.02=0.58 Question 2. a) I am dealt 3 cards from a standard 52 card deck. If an Ace is higher than a seven, what is the probability that all 3 cards are spades and are lower than a seven? 5 3 52 3 A S B D C

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b) I am dealt 3 cards from a standard 52 card deck. Given that I got a three card straight (that is, three consecutive cards, like 3, 4, 5, regardless of suit), what is
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IE111_Exam1a_solutions - IE 111 9:00 Section Exam 1 Fall...

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