one of, so the answer is
13
·
12
4
4
4
1
52
5
.
Example.
What is the probability that in a poker hand we get exactly 3 of a kind (and he other two cards
are of different ranks)?
Answer.
The probability of 3 aces, 1 king and 1 queen is
4
3
4
1
4
1
52
5
. We have 13 choices for
the rank we have 3 of and
12
2
choices for the other two ranks, so the answer is
13
12
2
4
3
4
1
4
1
52
5
.
Example.
In a class of 30 people, what is the probability everyone has a different birthday?
(We assume
each day is equally likely.)
Answer.
Let the first person have a birthday on some day. The probability that the second person has a
different birthday will be
364
365
. The probability that the third person has a different birthday from the first
two people is
363
365
. So the answer is
1

364
365
363
365
· · ·
336
365
.
Example.
Suppose 10 people put a key into a hat and then withdraw one randomly. What is the probability
at least one person gets his/her own key?
Answer.
If
E
i
is the event that the
i
th person gets his/her own key, we want
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 Spring '09
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 Conditional Probability, Probability, Grammatical person

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