Please solve and show work IB style for 11 and 12 and 19 and 20. The answer key is attached but the numbering is skewed. However, there is no answer in the answer key for 11 e. I tried to correct the numbering.

\f36 (1 mark) Tower hears reply b 6 _1 (1 mark) Ship hears 4 6 C (1 mark) 36 Tower does not hear reply 2X_L- (1 mark) 36 18 Ship does not hear e (1,6). (2, 5). (3,4). (4,3). AL- (2 marks) (5,2).(6,1) or using a lattice diagram le conte. . 6 _1 36 6 (2 marks) 3_9 (2 marks) C 1 50 (1 mark) 20 100 2 f since independent 9 90 1- 11 (1 mark) (1 mark) (2 marks) 20 20 100 10 ifi 40 2 8 P(R5 U B5) = (1 mark) P (ship not hear |tower has no reply) = 100 5 P(R5) + P(B5) - P(R5 B5) P (ship not hear ^ tower has no reply) d P(E F) = P(EnF) _10 _1 P (F) 40 4 1 1_1 1 or using a P (tower has no reply 6 6 36 36 (2 marks) lattice diagram (2 marks) S (2 marks) e If independent then h Considering the list in e P(An B) = 0 so events P(E|F) = P(E) (1 mark) e 2 = - or using conditional are mutually exclusive 6 3 (2 marks) 1 60 4 - so not independent probability formula 30x2 = 18 100 (2 marks) (1 mark) (2 marks) Independent 6 50x= = 20 (2 marks) P(FOR) = P(F) X P(R) catch 20% (1 mark) C TX= = 30 = T=50 (2 marks) injected 30% 1 1x - so not 6 3 4 38 . Let x be the number not catch 80% independent 1 mark) speaking both English and French. catch 90% P(F UR) = P(F) + P(R) - P(F ~ R) (60-x)+x+(40-x)+10 = 100 not Injected 70% (1 mark) =110-x = 100 = x =10 1 1 1_5 (2 marks) 3 4 6 12 (1 mark) not catch 10% (4 marks) (2 marks layout P(exactly one team) = 2 marks numbers) 5 1_ 1 (2 marks) 12 6 4 70 90 63 50 10 30 10 Could also use a Venn 100 100 100 (1 mark) diagram in (b) and (c). 30 80 6 d P ( FOR| F ) = - P(FOR) 6=1 100 100 25 (1 mark) P(F) -2 A3 30 20 70 90 69 (2 marks) (1 mark shape 2 marks 100 100 100 100 100 14 48 a numbers) (2 marks) 689ANSWERS IT ant. .. . Is. cont. 122 61 (1 mark) Exercise 94 P(PC) - P(7'nC)_ _ 2 200 100 P(C) 23 92 23 (1 mark) (2 marks) 200 50 3 2able 4 21712 82 118 59 6 27r's" P(IC) = -P(InC) 1 - 24 200 200 100 2 marks) P(C') 8 x14y 20 3 or by using the 12 marks) 48 12 formula (2 marks) 9 12 1 9x4y 12 1 0a* 22 42 marks 14 Exercise 98 8 RG or GR 15 * V7 b /2' V6' 28 12 marks (60) 5 5 25 ( 3x) 8 8 65 42 marks V.x' (4 marks) (Al shape. 3 marks. I RG or GR 3, 3 3 5 15 42 3 7 numbers. 42 marks 32 2 a 10- 4 numbers, I mark 2 numbers) 12 marks) (5x ) 1 D 200-140-60 12 marks) . (2d) 4 f 3.x3 3 x 2 30 200 20 (1 mark) Exercise 9C 2 20 8 1 P(A B) AND- PLANB) P(B) 0.5 2 " P(AnB) = 0.2 (2 marks) " P(A) = P(An B)+ P(An8) = 0.2+0.4 =0.6 (2 marks) 7 "P(AVB) = P(A)+P(8)-P(A~.B)= 0.6+0.5-0.2=0.9 (2 marks) Exercise 90 NV P(A B)= P(AnB') 0.4 a Growth b Decay 2 = 0.8 P[B') 0.5 (2 marks) c Decay d Decay . Growth b PAJA) . P(A|B' ) so not independent (2 marks) 2 (x) = D g(x) = C hix) = A its = B jux) = E . . . . . . . . ....... ................. ..... Chapter 9 Skills check 1 a 32 b 1000 125 d 243 216 IN y'=4 V X E R. y > 4 690Exam-style questions 11 P1: An ordinary, fair, six-sided dice is thrown. Find the probability of obtaining a a five (1 mark) b an even number (1 mark) probability c a prime number Statistics and (2 marks) d a number greater than 3 and smaller than 6 (2 marks) e a number exactly divisible by 7. (1 mark) 12 P1: Two ordinary, fair, six-sided dice are thrown. One dice is red and the other is blue. Find the probability that a both dice are a 5 (1 mark) b both dice are the same number (1 mark) c the red dice is a 5 and the blue dice is a 4 (1 mark) d one dice is a 5 and the other a 4 (1 mark) e the total of the two dice is 7 (2 marks) f the red dice is a 5 given that the blue dice is a 4 (1 mark) 3898 a Sketch a probability tree that 19 P2: Adrian has a box with 5 red and 3 green represents all this information. apples in it. He takes out an apple at (4 marks) random and eats' it. He then takes out Find the probability that a random another apple at random and also eats it. person is not injected and catches the a Find the probability that he eats disease. (1 mark) i two red apples Find the probability that a random ii two apples of different colours. person is injected and does not catch the disease. (1 mark) (4 marks) d Find the probability that a random Sally also has a box with 5 red and 3 person does catch the disease. green apples in it. Sally is on a diet. She (2 marks) takes out an apple at random and then puts it back in the box. She then takes e Given that a random person out another apple at random. has caught the disease find the probability that they were not b Find the probability that she takes injected. (2 marks) i two red apples f Given that a random person has ii two apples of different colours. not caught the disease find the (4 marks) probability that they were injected. (2 marks) 20 P1: a For two events, A and B, 18 P1: A college with 200 students offers P( B) = 0.5, P( A|B) = 0.4 and rowing, kayaking and surfing as P(An B') = 0.4. activities. Of the students, 8 do all three Calculate activities, 30 do rowing and kayaking, 20 do rowing and surfing, 10 do surfing i P(An B) and kayaking but not rowing, 40 do ii P( A) only rowing, 70 do kayaking and 48 do surfing. ili P( A U B) a Sketch a Venn diagram to represent iv P( A B' ) (8 marks) Statistics and probability all this information. In each enclosed b Determine, with a reason, whether space in the diagram put the number events A and B are independent or of students that this space specifically not. refers to. (4 marks) (2 marks) Calculate how many students do not do any of these three activities. (2 marks) c If a student is chosen at random find the probability they i do only kayaking ii do rowing or kayaking iii do rowing or kayaking but not surfing iv do not do rowing. (5 marks) d Given that a student does surfing find the probability that they also do rowing. (2 marks) 391