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Steven Weber
Dept. of ECE
Drexel University
ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010)
Recitation 1 Solutions
Let
k,l
be integers with 1
≤
l
≤
k
. Assume the sex of a child is unaﬀected by the sexes of any siblings and that
each child is equally likely to be a boy or a girl. Note there are 2
k
possible gender assignments for
k
children. The
two optional questions require the use of the binomial coeﬃcient
(
s
r
)
, the number of ways of selecting an unordered
subset of
r
objects from a set of
s
distinct objects.
1.
A family has three children. What is the probability that all three are girls given that at least one is a girl?
1
7
(1)
There are seven possibilities for three children with at least one girl, of these one is all girls.
2.
A family has
k
children. What is the probability that all
k
are girls given that at least one is a girl?
1
2
k

1
(2)
There are 2
k

1 possibilities for
k
children with at least one girl, of these one is all girls.
3.
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This note was uploaded on 06/10/2010 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.
 Spring '04
 Eisenstein

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