Question text Guidelines to answer the following question: Fill in the blanks with the correct answers. Do NOT use any spaces or brackets. For all numerical answers, give EXACT values (i.e. do not round your answers) unless instructed otherwise in the question. If using fractions, give answers as SIMPLIFIED fractions using the forward slash (e.g. 1/2 or 5/4). Use - for any negatives. ______________________________________________________________________________________________ This question is worth 4 + 1 + 2 + 4 = 11 marks. Anita owns a bike and a  car. Let event [math: B] be that Anita uses her bike during the week, and event [math: C] be that she uses her car during the week. It is known that [math: Pr(B)=0.5], [math: Pr(C)=0.7] and [math: Pr(B∩C)=0.4]. a. Complete the following probability table representing this information. Give all values to 1 decimal place. (4 marks) [table] | C | C' | Total B | Answer 1 Question 6 | Answer 2 Question 6 | Answer 3 Question 6 B' | Answer 4 Question 6 | Answer 5 Question 6 | Answer 6 Question 6 Total | Answer 7 Question 6 | Answer 8 Question 6 | 1 [/table] b. Using the table, state the probability that Anita uses her car but not her bike. Give your answer to 1 decimal place. Answer: Answer 9 Question 6[input] (1 mark) c. Calculate the probability that Anita uses her bike given that she uses her car. Complete the following by filling in numerical answers, and give your final answer correct to 2 decimal places. Pr[math: (B|C)] [math: =] Answer 10 Question 6[input] [math: ÷] Answer 11 Question 6[input] [math: =] Answer 12 Question 6[input] (2 marks) d. Anita’s company does a survey of all staff to identify how they travel to work. There are 150 members of staff, and the following results are obtained. Pr(C) = 0.22 Pr(T) = 0.7 Pr(C ∩ T) = 0.12 where C represents travel by car, and T represents travel by train. (4 marks) i. How many of the staff surveyed travel by train? Answer: Answer 13 Question 6[input] ii. Show the equation to find the probability that a randomly selected staff member travels by car, train, or both. Answer 14 Question 6[select: , Pr(C), Pr(T), Pr(C ∩ T), Pr(C U T)] [math: =] Pr(C) [math: +] Answer 15 Question 6[select: , Pr(C), Pr(T)] [math: −] Answer 16 Question 6[select: , Pr(C), Pr(T), Pr(C ∩ T), Pr(C U T)] iii. Calculate the probability that a randomly selected staff member travels by car, train, or both. Answer: [math: Pr(car,train,orboth)=] Answer 17 Question 6[input]多项填空题