Please solve and show work IB style for 19 and 20. The answer key is attached but the numbering is skewed. I tried to correct the numbering.

ANSWERS 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 6908 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