ISDS361A
Solutions 2.
Probability, Counting, Binomial Distribution
Panayiotis Skordi
1.
Let x represent the number of times a student visits a bookstore in a one month
period. Assume that the probability distribution of x is as follows:
x
0
1
2
3
p(x)
0.05
0.25
0.50
0.20
a. Find the mean
μ
.
b. What is the probability that the student visits the bookstore at least once in a
month?
c. What is the probability that the student visits the bookstore at most twice a
month?
Solution 1
a.
∑
=
=
=
n
i
i
i
x
P
x
x
E
1
)
(
)
(
μ
in our case n has 4 values 0, 1, 2 , 3 . So we add
85
.
1
20
.
0
*
3
50
.
0
*
2
25
.
0
*
1
05
.
0
*
0
=
+
+
+
=
b. At lest once in a month tells us either 1 or 2 or 3 times in a month.
So we need
95
.
0
20
.
0
50
.
0
25
.
0
)
3
(
)
2
(
)
1
(
=
+
+
=
+
+
P
P
P
c. At most twice means 0 or 1 or 2
So we need
80
.
0
50
.
0
25
.
0
05
.
0
)
2
(
)
1
(
)
0
(
=
+
+
=
+
+
P
P
P
1
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View Full Document2.
In a race with 8 runners how many runners can finish first, second and third?
Solution 2
The order obviously is important here. We will use the formula for permutations.
)!
(
!
r
n
n
P
r
n

=
where n is 8 and r is 3
336
120
40320
!
5
!
8
)!
3
8
(
!
8
)!
(
!
=
=
=

=

=
r
n
n
P
r
n
ways.
3.
A combination lock has a total of 30 numbers and will unlock with the proper 4
number sequence. How many possible combinations are there?
Solution 3
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 Fall '07
 Skordi
 Normal Distribution, Probability theory, Binomial distribution

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