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(AB)=0.1.
Suppose also that B and D are independent.
(Please
compute a final probability (a number) for each part).
a)
Find P(BC)
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)=0.7P(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+0.2P(AB)P(B)=0.60.02=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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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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 Spring '07
 Storer
 Probability, Playing card, Card game

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