LESSON 12.1 Use lists, tables and tree diagrams to represent sample spaces I can use the Fundamental counting Principle to count outcomes

experiment outcomes outcome trial event experiment sample space tree diagram

H H T T T H HT H T H H T T H T H T H T H T H H T T H T

H 1 H 2 H 3 H 4 H 5 H 6 T 1 T 2 T 3 T 4 T 5 T 6 H T H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6

K R D C NC C C P NP P P P P P kids with cheese and pickles 12 different orders possible 3 ⦁ 2 ⦁ 2 = 12

N1 ⦁ N2 ⦁ N3 ⦁ …..

10 ⦁ 2 ⦁ 12 ⦁ 5 ⦁ 20 ⦁ 20 ⦁ 2 = 960,000

11 ⦁ 7 ⦁ 5 ⦁ 3 ⦁ 6 ⦁ 4 ⦁ 3 = 83,160

12-1 worksheet ASSIGNMENT

LESSON 12.2 I can use permutations with probability I can use combinations with probability

n! 4 ⦁ 3 ⦁ 2 ⦁ 1 = 24 10! = 10 ⦁ 9 ⦁ 8 ⦁ 7 ⦁ 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 = 3,628,800 5! = 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 = 120

order n P r n! (n – r)! 5 P 2 = 5! (5 – 2)! = 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 3 ⦁ 2 ⦁ 1 = 20 6 P 4 = 6! (6 – 4)! = 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 2 ⦁ 1 = 360

10 P 4 = P 3 =336

order n C r n! r!(n – r)! 10 C 4 = 10! 4! (10 – 4)! 10 ⦁ 9 ⦁ 8 ⦁ 7 ⦁ 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 4 ⦁ 3 ⦁ 2 ⦁ 1 = ⦁ 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ = 210

5 C 2 = 5! 2! (5 – 2)! = 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 2 ⦁ 1 ⦁ 3 ⦁ 2 ⦁ = 10

8 P 3 = C 3 = C 5 =5,461, C 4 = P 4 = 24

1 20 C 6 = 1 38, P 2 = 1 380

1 26 C 5 = 1 65, P 2 = 1 870

12-2 worksheet ASSIGNMENT

LESSON 12.3 I can solve problems involving geometric probability I can solve problems involving sectors and segments of circles

chance Area of B Total area

Area of square Total area = 4 28 = 0.14

Area of shaded Total area = = 0.48

P(red) = = 0.222

P(blue) = = 0.333

π (2 2 ) = 4 π – π (1 2 ) = 1 π = 3 π (area of white region) π (3 2 ) = 9 π (area of target) P(white) = 3π3π 9π9π = 0.333

π (6 2 ) = 36 π – π (3 2 ) = 9 π = 27 π (area of blue region) π (6 2 ) = 36 π (area of target) P(blue) = 27 π 36 π = 0.75

12-3 worksheet ASSIGNMENT

LESSON 12.4 I can find the probabilities of independent and dependent events I can find the probability of events given the occurrence of other events

2 or more does not affects

independent dependent independent

dependent

P(A and B) = P(A) ⦁ P(B) ⦁ 1 6 = 1 36

⦁ 1 3 = 1 9

P(A and B) = P(A) ⦁ P(B | A)

P(regular 1 st and 2 nd ) 8 13 ⦁ 7 12 =

TV VVVC 3 10 ⦁ 1 9 = ⦁ 5 9 = 30 90

12-4 worksheet ASSIGNMENT

LESSON 12.5 I can find the probabilities of events using two-way frequency tables

P(male) =20/30 P(female) =10/30 P(11th) = 12/30 P(12th) =18/30

/12 6/10 12/18 0

20% 15.6% 36.9% 47.5% 52.5% 43.1% 56.9% 100% 47.5% of (285) ≈ 135 students 44/76 ≈ 0.579

12-5 worksheet ASSIGNMENT

LESSON 12.6 I can find probabilities of events that are mutually exclusive and events that are not mutually exclusive

mutually exclusive yes no

yes

P(A or B) = P(A) + P(B) = 22 35

= =

P(A or B) = P(A) + P(B) – P(A and B) P(H or K) = P(H)+ P(K) –P(H and K) = – 1

P(~A) = 1 – P(A) ~A: rolling an even number ~B: picking heart, diamond or spade ~C: losing or tying a game P(A) = 3/6 P(~A) = 3/6 P(B) = 13/52 P(~B) = 39/52 P(C) = 0.7 P(~C) = 0.3

= 4 6

= 4 6 – 1 6

12-6 worksheet ASSIGNMENT