\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) 689Exam-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) 389