(See Example 3.)
Monitoring Progress and Modeling with Mathematics
Monitoring Progress and Modeling with Mathematics
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Section 13.2
Independent and Dependent Events
719
12.
PROBLEM SOLVING
You play a game that involves
drawing three numbers from a hat. There are
25 pieces of paper numbered from 1 to 25 in the hat.
Each number is replaced after it is drawn. Find the
probability that you will draw the 3 on your first draw
and a number greater than 10 on your second draw.
13.
PROBLEM SOLVING
A drawer contains 12 white
socks and 8 black socks. You randomly choose 1 sock
and do not replace it. Then you randomly choose
another sock. Find the probability that both events
and
B
will occur.
(See Example 4.)
NUMBER SENSE
Events
A
and
B
are dependent.
Suppose
P
(
B A
)
=
0.6 and
P
(
A
and
B
)
Find
P
(
A
).
19.
ANALYZING RELATIONSHIPS
You randomly select
three cards from a standard deck of 52 playing
cards. What is the probability that all three cards are
face cards when (a) you replace each card before
selecting the next card, and (b) you do not replace
each card before selecting the next card? Compare the
probabilities.
(See Example 5.)
20.
ANALYZING RELATIONSHIPS
A bag contains 9 red
marbles, 4 blue marbles, and 7 yellow marbles. You
randomly select three marbles from the bag. What
is the probability that all three marbles are red when
A
14.
PROBLEM SOLVING
A word game has 100 tiles,
98 of which are letters and 2 of which are blank.
The numbers of tiles of each letter are shown.
You randomly draw 1 tile, set it aside, and then
randomly draw another tile. Find the probability
that both events
A
and
B
will occur.
:
:
15.
ERROR ANALYSIS
Events
A
and
B
are independent.
Describe and correct the error in finding
P
(
A
and
B
).
0.2
16.
ERROR ANALYSIS
A shelf contains 3 fashion
magazines and 4 health magazines. You randomly
choose one to read, set it aside, and randomly choose
another for your friend to read. Describe and correct
the error in finding the probability that both events
and
B
occur.
A
—
=
7
P
(
A
and
B
)
=
3
7
⋅
4
—
7
=
12
—
49
≈
0.245
—
17.
NUMBER SENSE
Events
A
and
B
are independent.
Suppose
P
(
B
)
=
0.4 and
P
(
A
and
B
)
=
0.13. Find
P
(
A
).
18.
NUMBER SENSE
Events
A
and
B
are dependent.
Suppose
P
(
B A
)
=
0.6 and
P
(
A
and
B
)
Find
P
(
A
).
19.
ANALYZING RELATIONSHIPS
You randomly select
three cards from a standard deck of 52 playing
cards. What is the probability that all three cards are
face cards when (a) you replace each card before
selecting the next card, and (b) you do not replace
each card before selecting the next card? Compare the
probabilities.
(See Example 5.)
20.
ANALYZING RELATIONSHIPS
A bag contains 9 red
marbles, 4 blue marbles, and 7 yellow marbles. You
randomly select three marbles from the bag. What
is the probability that all three marbles are red when
=
0.15.