Target fitness is an international company that owns and operates many fitness centres in several countries. At every one of Target fitness's fitness centre, each

member agrees to have his or her fitness assessed every month by undertaking a set of exercises called S. There is a five-minute time limit on any attempt to complete S and if someone completes S in less than three minutes, they are considered fit. At Target fitness center in Singapore, it has been found that the probability that any member will complete S in less than three minutes is 5 8. This is independent of any other member. In a particular week, 10 members of this fitness centre attempt S. (a) Find the probability, that at least 9 of these 10 members will complete S in less than three minutes. (3 marks) (b) Given that at least 9 of these 10 members complete S in less than three minutes, what is the probability that exactly 9 of them complete S in less than three minutes. (3 marks)

2. Target fitness is an international company that owns and operates many fitness centres in several countries. At every one of Target fitness's fitness centre, each member agrees to have his or her fitness assessed every month by undertaking a set of exercises called S. There is a five-minute time limit on any attempt to complete S and if someone completes S in less than three minutes, they are considered fit. At Target fitness center in Singapore, it has been found that the probability that any member will complete S in less than three minutes is 2. This is independent of any other member. In a particular week, 10 members of this fitness centre attempt S. (a) Find the probability, that at least 9 of these 10 members will complete S in less than three minutes. (3 marks) (b) Given that at least 9 of these 10 members complete S in less than three minutes, what is the probability that exactly 9 of them complete S in less than three minutes. (3 marks) Hint: To simplify the expression take common factors out