Theory of Probability, HW #1, all sections
Assignment Date: March 4, 2011;
Due Date: March 11,2011
1.
The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a 2, 3, or 12, the player loses; if the
sum is either a 7 or an 11, he or she wins. If the outcome is anything else, the player continues to roll the dice until he or she
rolls either the initial outcome or a 7. If the 7 comes first, the player loses; whereas if the initial outcome reoccurs before the 7,
the player wins. Compute the probability of a player winning at craps.
Hint
: Let
g1831
g3036
denote the event that the initial outcome is
i
and the player wins. The desired probability is
∑ g1842(g1831
g3036
)
g2869g2870
g3036g2880g2870
.
To compute
g1842(g1831
g3036
),
define the events
g1831
g3036,g3041
to be the event that the initial sum is
i
and the player wins on the
n
th roll. Argue that
g1842(g1831
g3036
)=∑ g1842g3435g1831
g3036,g3041
g3439
∞
g3041g2880g2869
.
2.
We have a stick of 9 consecutive parts. Each part is painted red or white. If none of the neighboring parts are painted white, how
many different painting patterns can be done?
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 Spring '11
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 Probability, initial outcome

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