Name ________________________________________ Date __________________ Class __________________
LESSON
22-2
Independent Events
Reading Strategies: Draw Conclusions
Two events are independent when the occurrence of one event does not
affect the occurrence of the other event. You can use your understanding
of probability to draw a conclusion as to whether or not two events, A and
B, are independent.
Does P ( A ∩ B ) = P ( A ) i P (B )?
yes
A and B are
independent.
P(A | B) =
Does P(A | B) = P(A)?
no
yes
A and B are
not
independent.
Remember,
P(A ∩ B)
.
P (B )
no
A and B are
independent.
A and B are
not
independent.
For each pair of events, answer one of the questions above. Show
your work. Then write independent or not independent to state your
conclusion.
1. A jar contains 16 blue marbles and 20 green marbles. You randomly
draw one marble from the jar. You put that marble back in the jar and
randomly draw a second marble from the jar.
Let B be the event that you draw a green marble first.
Let G be the event that you draw a blue marble second.
___________________________
2. The two-way frequency table shows the students on a high school
track team who compete in two different types of races.
Juniors Seniors Total
Relay
5
3
8
10K
6
6
12
Total
11
9
20
Let R be the event that a team member competes in relay races.
___________________________
Let J be the event that a team member is a junior.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
425
4.
32
729
5.
8
243
1.
1
4
6.
8
729
2.
1
4
7.
2
9
3.
1
36
8.
1
54
4.
9
100
9.
1
54
5.
3
20
10.
1
216
6.
1
10
7.
3
10
Practice and Problem Solving:
Modified
Practice and Problem Solving: C
1.
1
25
8.
2.
1
16
1
36
9.
3.
1
28,561
1
9
10.
4.
15
4,802
1
36
11.
5.
15
9,604
1
12
Reading Strategies
6.
9
2,401
7.
9
4,802
8.
5
18
1. Independent; Possible work:
20
20 i 16
P (B ∩ G ) =
, P (B ) =
, and
36
36 i 36
16 20 i 16 20 16
P (G ) =
i
=
i
, so
36 36 i 36 36 36
P (B ∩ G ) = P (B ) i P (G ) .
2. Not independent; Possible
2
5
and P (R ) = .
work: P (R | J ) =
5
11
5 2
≠ , so P (R | J ) ≠ P (R ) .
11 5
7
9.
18
10.
2
9
11.
1
9
Success for English Learners
1. No; if the marble had not been put back,
the total number of marbles in the jar
would have been affected. So, the
occurrence of drawing a green marble
second would have been affected. The
events would not be independent.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
545