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. Charlie exercises each week by going to the gym and doing yoga. Let event [math: G] be that he goes to the gym and event [math: Y] be that he does yoga. It is known that [math: Pr(G)=0.65], [math: Pr(Y)=0.40] and [math: Pr(G∩Y)=0.30] a. Complete the following probability table representing this information. Give all values to 2 decimal places. (4 marks) [table]
| G | G' | Total Y | Answer 1 Question 6 | Answer 2 Question 6 | Answer 3 Question 6
Y' | 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 your table, state the probability that in a particular week, Charlie does Yoga but not gym. Answer: Answer 9 Question 6[input] (1 mark) c. Calculate the probability that Charlie goes to yoga, given that he goes to the gym. Complete the following by filling in numerical answers, and give your final answer correct to 2 decimal places. Pr[math: (Y|G)] [math: =] Answer 10 Question 6[input] [math: ÷] Answer 11 Question 6[input] [math: =] Answer 12 Question 6[input] (2 marks) d. Charlie is also a member of a local running club, which has a total of 200 members. The club do a survey of the additional fitness activities undertaken by their members, with the following results. Pr(G) = 0.72 Pr(Y) = 0.15 Pr(G ∩ Y) = 0.09 where G represents going to the gym, and Y represents going to yoga. (4 marks) i. How many members do yoga? Answer: Answer 13 Question 6[input] ii. Show the equation to find the probability the members going to the gym, yoga or both. Answer 14 Question 6[select: , Pr(G), Pr(Y), Pr(G ∩ Y), Pr(G U Y)] [math: =] Pr(G) [math: +] Answer 15 Question 6[select: , Pr(G), Pr(Y)] [math: −] Answer 16 Question 6[select: , Pr(G), Pr(Y), Pr(G ∩ Y), Pr(G U Y)] iii. Calculate the probability that a randomly selected member goes to the gym, yoga or both. Answer: [math: Pr(gym,yoga,orboth)=] Answer 17 Question 6[input] Please answer all parts of the question.
