Question 3 - Blood Transfusion (5 marks) A blood transfusion is a routine medical procedure in...

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Question 3 - Blood Transfusion (5 marks) A blood transfusion is a routine medical procedure in which donated blood is provided to you through a narrow tube placed within a vein in your arm. Blood types are important when it comes to transfusions. If you get a blood transfusion that that is not compatible with your blood type, your body's immune system response will be triggered to fight the donated blood. For instance, a patient with Type O- blood can only receive Type O- blood, but a patient with Type O+ blood can receive either Type O+ or Type O-. Ethnic background is also important in blood transfusions. If a blood donor and recipient are of the same ethnic background, the chance of an adverse reaction may be reduced. According to a 10-year donor database of a particular country, 0.37 of white donors in the country are O+ and 0.08 are O-. a) Consider a random sample of 15 white donors in this country. What is the expected value of the number of individuals who could be a donor to a patient with blood type 0+, and what is the standard deviation? (2 marks) b) Calculate the probability that 3 or more of individuals in the sample from part (a) could donate blood to a patient with O- blood type. (1 mark) c) On average, how many donors would need to be randomly sampled for the first type 0+ donor to be identified? Assume that only while individuals are being tested. (1 mark) d) What is the probability that exactly 4 donors must be sampled to identify the first type O+ blood? Assume that only while individuals are being tested. (1 mark) Question 3 - Blood Transfusion (5 marks) A blood transfusion is a routine medical procedure in which donated blood is provided to you through a narrow tube placed within a vein in your arm. Blood types are important when it comes to transfusions. If you get a blood transfusion that that is not compatible with your blood type, your body's immune system response will be triggered to fight the donated blood. For instance, a patient with Type O- blood can only receive Type O- blood, but a patient with Type O+ blood can receive either Type O+ or Type O-. Ethnic background is also important in blood transfusions. If a blood donor and recipient are of the same ethnic background, the chance of an adverse reaction may be reduced. According to a 10-year donor database of a particular country, 0.37 of white donors in the country are O+ and 0.08 are O-. a) Consider a random sample of 15 white donors in this country. What is the expected value of the number of individuals who could be a donor to a patient with blood type 0+, and what is the standard deviation? (2 marks) b) Calculate the probability that 3 or more of individuals in the sample from part (a) could donate blood to a patient with O- blood type. (1 mark) c) On average, how many donors would need to be randomly sampled for the first type 0+ donor to be identified? Assume that only while individuals are being tested. (1 mark) d) What is the probability that exactly 4 donors must be sampled to identify the first type O+ blood? Assume that only while individuals are being tested. (1 mark)