Transcript 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
PE
number of possible outcomes in S
nS
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