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IE111_Exam1b_solutions

# IE111_Exam1b_solutions - IE 111 10:00 Section Exam 1 Fall...

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IE 111 Solutions 10:00 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|D)=0.1. Suppose also that B and D are independent. (Please compute a final probability (a number) for each part). a) Find P(C|B) =1, since if B happens, then C necessarily happens b) Find P(B ′∩ C) =P(C)-P(B)=0.1 c) Find P(A ′∩ B ′∩ D) =P(D)-P(A D)=P(D)-P(A|D)P(D)=0.63 d) Find P(A D) =P(A)+P(D)-P(A|D)P(D)=1.03, so there must be some problem with the data. (My apologies.) e) Find P(A B) =P(A)+P(B)=0.6 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 lower than a seven? 20 3 52 3 D A C B S

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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 the probability that my hand contains a six? (note: both Queen King Ace and Ace Two Three are considered straights).
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