Geometric Probability

Geometric probability uses ideas about area to find the probability of an event.

( ) Area Total

Area Shaded=shadedP

If a parachutist jumps out of a plane, what is the probability he will land on the emblem of a Football Field?

The parachutist guarantees that he will land on the field or the jump is at NO cost.

Area of Emblem=(80)(80) Area of Field = (160)(360)

Probability

P = (80)(80)/(160)(360)P = 6400/57,600P = 1/9

Probability

Roulette26

23 1

16

206

12

17

19

14

28

10

30

9

721 3

25

24

13

15

18

27

2

11

29

8

22

4

5

ODD   EVEN

1 11 21

2 12 22

3 13 23

4 14 24

5 15 25

6 16 26

7 17 27

8 18 28

9 19 29

10 20 30

1 to 10 11 to 20 21 to 30

RED   BLACK

P(odd number)

P(1 to 10)

P(Black)

P(number 1)

= 15/30 = ½ or 50%

= 10/30 = 1/3 or 33%

= 15/30 = ½ or 50%

= 1/30 or 3.3%

Your turn, Find the probability of the red area.

20 ft

10 ft6 ft

1020

62

⋅ 200

36=50

9=

What is the probability of throwing a dart and hitting the red, blue, or yellow areas? Assume that every dart will hit within the large white square.

How large is the white area?

3636 ⋅=White 1296=

What is the probability of hitting the Red area?2 rA π=

( ) ( ) 26.283 14.3 2 ==redA

( )1300

30

1296

26.28 ≈=redP

( )130

3≈redP

What is the probability of hitting the blue area?

( ) ( ) 34.2549 14.3 2 ==blueA

( )1300

225

1296

08.226 ≈=blueP

( ) 08.22626.2834.254 =−=−redblueA

( )52

9≈blueP

What is the probability of hitting the yellow area?

( ) ( ) 5.70615 14.3 2 ==yellowA

( )1300

450

1296

16.452 ≈=yellowP

( ) 16.45234.2545.706 =−=−blueyellowA

( )26

9≈yellowP

Your turn, Find the probability of the red area.

5

1

200

40 ≈≈10 ft

20 ft

Geometric Probability