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(AD)=0.1.
Suppose also that B and D are independent.
(Please
compute a final probability (a number) for each part).
a)
Find P(CB)
=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(AD)P(D)=0.63
d)
Find P(A
∪
D)
=P(A)+P(D)P(AD)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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 Spring '07
 Storer
 Probability, Playing card, Card game

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