Question 1)Consider the following context:The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit. How many complete branches, from start to finish, would a tree diagram that models this context include? H Question 2)The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit. What is, therefore, the chance of a true positive outcome of this compound event: BOTH a positive result on the clinical diagnosis AND a positive result on the OTC kit diagnosis, given that the clinical diagnosis was positive? Question 3)Consider the following context:The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit. If 10% of the results from the OTC diagnostic kits are positive after the adult volunteers already tested positive with the clinical diagnosis, then what was the complementary probability for those OTC diagnostic kits that end up with negative results? Express the answer as a percentage without insignificant digits, with percent symbol.Question 4)The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit. [ What is, therefore, the chance of a false negative outcome of this compound event: BOTH a positive result on the clinical diagnosis AND a negative result on the OTC diagnostic kit, given that the result of the clinical diagnosis was positive for food allergies? HINTS: As a reminder, if 10% of those who tested positive with the clinical diagnosis also tested positive with the kit, what percentage surprisingly tested negative with the kit? Question 5)Consider the following context:The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit. If 25% of the positive results from the clinical diagnoses ended up as positive result of food sensitivity or intolerance, then what was the complementary probability for those adult volunteers who ended up with a negative result from the clinical diagnosis, apparently having no food insensitivies or allergies? Express the answer as a percentage without insignificant digits, with percent symbol.

Question

Question 1)Consider the following context:The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen.  Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit.  Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit.   How many complete branches, from start to finish, would a tree diagram that models this context include?  H Question 2)The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen.  Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit.  Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit.   What is, therefore, the chance of a true positive outcome of this compound event: BOTH a positive result on the clinical diagnosis AND a positive result on the OTC kit diagnosis, given that the clinical diagnosis was positive?  Question 3)Consider the following context:The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen.  Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit.  Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit.   If 10% of the results from the OTC diagnostic kits are positive after the adult volunteers already tested positive with the clinical diagnosis, then what was the complementary probability for those OTC diagnostic kits that end up with negative results?  Express the answer as a percentage without insignificant digits, with percent symbol.Question 4)The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen.  Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit.  Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit.  [ What is, therefore, the chance of a false negative outcome of this compound event: BOTH a positive result on the clinical diagnosis AND a negative result on the OTC diagnostic kit, given that the result of the clinical diagnosis was positive for food allergies?  HINTS: As a reminder, if 10% of those who tested positive with the clinical diagnosis also tested positive with the kit, what percentage surprisingly tested negative with the kit?  Question 5)Consider the following context:The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen.  Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit.  Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit.  If 25% of the positive results from the clinical diagnoses ended up as positive result of food sensitivity or intolerance, then what was the complementary probability for those adult volunteers who ended up with a negative result from the clinical diagnosis, apparently having no food insensitivies or allergies?  Express the answer as a percentage without insignificant digits, with percent symbol.

Accepted Answer

5.Given data
The nutrition and food science division of Farnsworth pharmaceuticals is alpha testing…