Assignment 2 Solutions;
MATH 203
Problem 3.24
(a) The sample points are a family with 2 Boys, a family with Boy and then a
Girl, a family with a Girl then a Boy, and a family with a 2 Girls.
(b) If having a Boy is equally likely to having a girl and vice versa, then:
Pr
(
Boy

Boy
) =
1
4
;
Pr
(
Boy

Girl
) =
1
4
Pr
(
Girl

Boy
) =
1
4
;
Pr
(
Girl

Girl
) =
1
4
.
(c) We can estimate the probabilities of these intersections with their sample prob
abilities.
ˆ
p
BoyBoy
=
1085
4208
= 0
.
258
ˆ
p
BoyGirl
=
1086
4208
= 0
.
258
ˆ
p
GirlBoy
=
1111
4208
= 0
.
264
ˆ
p
GirlGirl
=
926
4208
= 0
.
220
(d) There is not a large change in the probabilities from what we would expect
under equal probabilities. There deﬁnitely does not seem to be a bias for people
who have boys ﬁrst to have boys second. There seems to be a bit of a drop for
people who have girls ﬁrst to have boys second. This might indicate that more
that the overall probability of having boys is slightly higher, but not that it “runs
in the family”.
1
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View Full DocumentProblem 3.32
(a) Let the ﬁrst letter in a gene pair represent the gene from the ﬁrst parent and the
second letter represent the gene from the second parent. There are four possible
sample points for the gene pair for the child in the case of part (a): BB,bB,Bb,bb.
Because each of these sample points has probability 1/4, we know the probability
of a blueeyed child is 1/4. If you assume independence of the parents (implied
by the problems), if you let A be the event the ﬁrst parent contributes
a b
and C
be the event that the second parent contributes
a b
, then
Pr
(
bb
) =
P
(
A
∩
C
) =
P
(
A
)
P
(
C
) =
1
2
×
1
2
=
1
4
.
(b) In this example, we have possible combinations (denoting the two genes for
the second parent as
b
1
and
b
2
):
Bb
1
,
bb
1
,
Bb
2
,
bb
2
. Therefore, the probability
of a blueeye child is now 1/2. Also can show using the events of part (a) with
Pr
(
bb
) =
Pr
(
A
∩
C
) =
Pr
(
A
)
Pr
(
C
) = (1
/
2)(1) = 1
/
2.
(c) Because one parent has only BB pair, the probability of getting a bb pair is 0.
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 Summer '08
 Dr.JoseCorrea
 Math, Statistics, Probability, Probability theory, homemade weapon

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