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

number of possible outcomes in

n EEP E

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.

b. in two draws without replacement you get two good batteries.

good batteries

batteries

n

n8 2

12 3

ways to get 2 good

ways to draw 2 batteries

n

n

8,2

12,2

C

C

8,1

12,1

C

C

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.

b. One ball is red and two are black.

3,3

8,3

C

C

draw 3 green

draw 3

n

n1

56

draw 1 red, 2 black

draw 3

n

n

2,1 3,2

8,3

C C

C

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.

3,21

11,2

C

C

3 521

55 55

1 both yellowP