Download Section 7.4

Section 7.4
Use of Counting Techniques in
Probability
Computing the Probability of an
Event in a Uniform Sample Space
Let S be a uniform sample space and let E be any
event. Then
number of favorable outcomes in E n  E 
PE 

number of possible outcomes in S
nS 
Ex. Suppose that you reach into a box of 12 size
AA batteries and you know that 4 of them are
dead. Find the probability that
a. in one draw you get a good battery.
n  good batteries 
n  batteries 

C  8,1
C 12,1
8 2


12 3
b. in two draws without replacement you get
two good batteries.
n  ways to get 2 good 
n  ways to draw 2 batteries 

C  8, 2 
C 12, 2 
28 14


66 33
Ex. Three balls are selected at random without
replacement from the jar below. Find the
probability that
a. All 3 of the balls are green.
n  draw 3 green 
n  draw 3

C  3,3
C  8,3
1

56
b. One ball is red and two are black.
n  draw 1 red, 2 black 
n  draw 3

C  2,1  C  3, 2 
C  8,3
6
3


56 28
Ex. Refer to the jar of marbles below. Two
marbles are drawn at random without
replacement.
Find the probability that no yellow are drawn.
1  P  both yellow   1 
C  3, 2 
C 11, 2 
3 52
 1

55 55