Tutorial 5 2021 semester 2 Section A Question 1 In a batch of 15 jars of instant coffee, 5 have been under filled. Suppose 6 of these jars are selected without replacement. If more than 1 of these selected jars are under filled, the whole batch is sent back for refill. What is the probability of the batch being sent back for refill? Question 2 An anonymous caller told the police that he saw a hit and run incident and had briefly seen the number plate of the car. He knew that the number plate started with two letters a B and an E but could not remember the order. After the letters were four digits 3, 4, 8 and 9 but again he could not remember the order. The four numbers were followed by the letter V. How many number plates will the police have to check to be sure of including the car involved in the hit and run incident? Questions 3 to 6 are based on the following information: A company has 5 products in it's Basics range, 5 products in it's Standard range and 4 products in it's Premium range. The company wishes to advertise in a local newspaper, but due to space constraints, it can only advertise 6 products. Question 3 How many possible 6-prouct groupings/selections are possible? Question 4 What is the probability that an advert of 6 randomly selected products contains an equal number of products from each of the ranges? Question 5 What is the probability that an advert of 6 randomly selected products contains the whole Basics range and one item from the Standard range? Question 6 What is the probability that an advert of 6 randomly selected products contains the whole Basics range? Section B Let K denote the event that a person knows how to knit and let N denote the event that a person does not know how to do needle-work. Question 7 Describe in words the. event that is represented by the shaded area on the diagram below. Question 8 Describe in words the event that is represented by the shaded area on the diagram below. Question 9 Describe in words the event that is represented by the shaded area on the diagram below. Section C Question 10 Let A and B be events defined on the same sample space. Identify which of the statements below are true and which are false. a) IfA and B are mutually exclusive then they are independent. b) lfA and B are independent then they are not mutually exclusive. c) IfA and B are independent, then the following is definitely true: P(A n B) = 0 Questions 11 and 12 are based on the following information: Suppose A and B are mutually exclusive events defined on the same sample space such that P(A)=O.37 and P(B)=c. Question 11 What is the maximum value of 6? Question 12 What is P(A |B)? Questions 13 and 14 are based on the following information: Suppose A and B are two events defined on the same sample space such that P(A) : 0.4 , PM U B) = 0.8 , P(B) : p where O