MAT140: Applied Statistical Methods
Introductory Probability Class Examples for Sections 4-1 through 4-5 – Solutions
{
1. a.
b.
{(
c.
{
d.
{
}
)(
)(
)(
)(
)(
)(
)(
)(
)(
)(
)(
)}
}
}
2. a. Sample Space:
Odd Primes:
{
{
}
}
( )
( )
( )
( )
( )
b. Sample Space: ( )
Face Cards: ( )
( )
c. Sample Space:
Non-Primes:
{
{
}
}
( )
( )
( )
( )
(can also be expressed as
( )
d. Sample Space:
{
Vowels:
{
}
or
)
}
( )
( )
( )
( )
( )
Prof. Fowler
e. Sample Space: ( )
Females: ( )
( )
( )
( )
3. a. Sample Space:
( )
Red cards:
cards
Multiples of : {
Both red and multiple of : {
(
} in each of
cards
)
b. Sample Space:
( )
Face cards:
cards
Spades:
cards
Both face card and spade: {
(
} of Spades
cards
)
c. Sample Space:
( )
Total of at Least : {
) (
)}
: {(
)}
: {(
(
suits
cards
} of Diamonds and Hearts
}
)
Prof. Fowler
d. Sample Space:
Total of at Most
( )
: {
}
Complement of “At Most
”: “At Least
Total of at Least : {
) (
)}
: {(
)}
: {(
(
)
(
)
e. Sample Space:
Total of : { (
”
}
(
)
( )
) (
) (
) (
)}
( )
f. Sample Space:
( )
: {
Total of No More Than
}
Complement of “No More Than
Total of at Least : {
) (
: {(
)}
: {(
(
)
(
)
)}
(
”: “At Least
”
}
)
Prof. Fowler
g. Probability of selecting a female as the first student:
Probability of selecting a male as the second student after selecting a female first:
Probability of selecting a male as the third student after selecting a female first and a male
second:
Probability of selecting all students in succession as desired:
h. Probability of selecting a red block first:
Probability of selecting a green block after selecting a red block first and not replacing it:
Probability of selecting a blue block after selecting a red block first and a green block second
without replacing either of them:
Probability of selecting a green block after selecting a red block first, a green block second, and a
blue block third without replacing any of them:
Probability of selecting all blocks in succession as desired:
i. Probability of selecting a red block first:
Probability of selecting a green block after selecting a red block and replacing it:
Probability of selecting a blue block after selecting a red block first and a green block second and
replacing both of them:
Probability of selecting a green block after selecting a red block first, a green block second, and a
blue block third and replacing all of them:
Probability of selecting all blocks in succession as desired:
Prof. Fowler