Please solve and show work IB style for 13 and 14. The answer key is attached but the numbering is skewed. I tried to correct the numbering.

36 (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) 6898 QUANTIFYING RANDOMNESS: PROBABILITY g one of the dice is a 5 (2 marks) 15 P1: On average in Wales it rains on 3 days h one of the dice is a 5 given that the out of every 5 days. total of the two dice is 7. (2 marks) a Over a month, that has 30 days in 13 P1: The probability that James is selected it, calculate how many of these days would be expected to have rain. for the school football team is 1. The 3 (2 marks) probability that he is selected for the Over a period of 50 days, calculate how many days would not be school rugby team is -. The probability 4 expected to have rain. (2 marks) that he is selected for the both teams is _. c Calculate what length of time in a State, with a reason, whether the 6 days, would be expected to have 30 events of him being selected for days of rain in it. (2 marks) football and being selected for rugby 16 P1: At an international school with 100 are independent. (2 marks) students, 60 students speak English, 40 b Find the probability that he is selected speak French and 10 students speak for at least one team. (2 marks) neither of these two languages. c Find the probability that he is selected a Calculate how many students speak for exactly one team. (2 marks) both English and French. (2 marks) d Find the probability that he is b Sketch a Venn diagram to represent selected for both teams given that he this information. In each enclosed is selected for football. (2 marks) region put in the number of students corresponding to this region. 14 P1: A control tower sends a message to a (3 marks) ship. The probability that the ship hears Calculate the probability that a the message is -. The ship will reply student chosen at random if and only if it receives the message. If i speaks English but not French the ship replies, the probability that the ii speaks either English or French tower hears the reply is 3 iii does not speak English. 5 a Sketch a probability tree to represent (3 marks) this information. (2 marks) d Given that a student speaks French, b Hence find the probability that the find the probability that they also speak tower hears a reply to the message it English. (2 marks) sends. (2 marks) e Let E be the event that a student c Write down the probability that it speaks English and F be the event that does not hear a reply. (2 marks) a student speaks French. Determine with a reason if events E and F are d Given that the tower did not hear a independent or not. (2 marks) reply, find the probability that the ship did not hear the original message. 17 P2: A disease that spreads rapidly is about (2 marks) to arrive at a city with a very large number of inhabitants. If a person does e Events are defined as follows: not do anything, then the probability A: The ship does not hear the original that they will catch the disease is 90%. message. If they have taken a special injection B: The tower receives a reply. then the probability that they will catch State, with a reason, whether the two the disease reduces to 20%. Sadly only events A and B are mutually exclusive 30% of the population could afford the or not. (2 marks) injection and they were all injected. 390