1
Acey Deucey
•
Have a standard deck of 52 cards
Ranks of cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A
Three cards drawn (without replacement)
What is probability that rank of third card drawn is
between the ranks of the first two cards, exclusive?
o
E.g., if ranks of first two cards drawn are 4 and 9, then want
probability that third card is a 5, 6, 7 or 8
•
Solution setup
Let X = difference between rank of 1
st
and 2
nd
card
P(X = 0) = 3/51
o
After picking first card, there are 3 others with same rank
o
This is not really relevant.
Just a warmup to get you thinking!
Acey Deucey Solution
•
Solution
P(X =
i
) =
,
where 1
i
12
o
(13 –
i
) ways to choose two ranks that differ by
i
o
First card has 2/13 chance of being one of those 2 ranks
o
Second card is one of 4 cards (out of 51) that differ in rank by
i
Want:
o
Of remaining 50 cards, there are 4 cards of each (
i
– 1) ranks
51
4
13
2
)
13
(
i
)

first two
between
card
rd
3
(
)
(
12
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 Spring '09
 Probability theory, Aceydeucey, Acey Deucey, Acey Deucey Solution

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