Probability Of Independent And Dependent Events Worksheet Page 3
ADVERTISEMENT
1
2
3
4
5
6
7
8Page 1 of 2
GOAL
2
P
D
E
ROBABILITIES OF
EPENDENT
VENTS
Two events A and B are
dependent events
if the occurrence of one affects the
occurrence of the other. The probability that B will occur given that A has occurred
is called the
of B given A and is written P(B|A).
conditional probability
P R O BA B I L I T Y O F D E P E N D E N T E V E N T S
If A and B are dependent events, then the probability that both A and B occur is
P(A and B) = P(A) • P(B|A).
Finding Conditional Probabilities
E X A M P L E 5
The table shows the number of endangered and threatened animal species in the
Endangered Species
United States as of November 30, 1998. Find (a) the probability that a listed animal
is a reptile and (b) the probability that an endangered animal is a reptile.
Source: United States Fish and Wildlife Service
Mammals
Birds
Reptiles
Amphibians
Other
59
75
14
9
198
Endangered
8
15
21
7
69
Threatened
S
OLUTION
number of reptiles
3
5
P(reptile) =
=
≈ 0.0737
a.
total number of animals
4
7
5
number of endangered reptiles
b.
P(reptile|endangered) =
total number of endangered animals
1
4
=
≈ 0.0394
3
5
5
Comparing Dependent and Independent Events
E X A M P L E 6
You randomly select two cards from a standard 52-card deck. What is the probability
S
H
TUDENT
ELP
that the first card is not a face card (a king, queen, or jack) and the second card is a
Look Back
face card if (a) you replace the first card before selecting the second, and (b) you do
For help with a standard
not replace the first card?
52-card deck, see p. 708.
S
OLUTION
If you replace the first card before selecting the second card, then A and B are
a.
independent events. So, the probability is:
4
0
1
2
3
0
P(A and B) = P(A) • P(B) =
•
=
≈ 0.178
5
2
5
2
1
6
9
b.
If you do not replace the first card before selecting the second card, then A and B
are dependent events. So, the probability is:
4
0
1
2
4
0
P(A and B) = P(A) • P(B|A) =
•
=
≈ 0.181
5
2
5
1
2
2
1
732
Chapter 12 Probability and Statistics
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education