STAT 230
Test #2
Feb 1, 2006
3:30 – 4:15 pm
Name:
S I.D:
UWUserid:
Mark
/31
Circle your instructor and time slot:
1. McLeish (10:30)
2. Zhu (12:30)
3. Drekic (1:30)
[15]
1. A not very skillful dart player throws a dart at a dart board.
The probability he hits the
bull’seye is 0.10. Find:
(a) the probability he gets his first bull’seye on his seventh throw. What assumptions are
you making?
Assumptions
: All throws are independent of one another and the same probability of
hitting a bull’seye (i.e.,
p
= 0
.
10) applies to each throw.
P
(he gets his first bull’seye on his seventh throw) = (0
.
90)
6
(0
.
10)
≈
0
.
053
(b) the probability he gets his second bull’seye on his tenth throw.
Let
X
≡
the number of failed attempts before getting his second bull’seye, so that
X
has a negative binomial distribution with
k
= 2 and
p
= 0
.
10.
We want
P
(
X
= 8) =
(
8+2

1
8
)
(0
.
10)
2
(0
.
90)
8
=
(
9
8
)
(0
.
10)
2
(0
.
90)
8
≈
0
.
039
(c) the probability he gets at least two bull’seyes in ten throws.
Let
Y
≡
the number of bull’seyes obtained in ten throws, so that
Y
has a binomial
distribution with
n
= 10 and
p
= 0
.
10. We want:
P
(
Y
≥
2)
=
10
X
y
=2
10
y
¶
(0
.
10)
y
(0
.
90)
10

y
=
1

1
X
y
=0
10
y
¶
(0
.
10)
y
(0
.
90)
10

y
≈
0
.
264
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[10]
2. A box contains 5 red cards and 5 green cards.
First, a fair coin is tossed.
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 Winter '06
 various
 Normal Distribution, Probability, Probability theory, Binomial distribution, Cumulative distribution function, Professor Moriarty

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