Can we Trust Our Intuition?
You are the head of a hospital's blood bank. A new patient, Mr. R, is admitted with a rare blood type. The hospital's blood bank has a 99% accurate record of blood types. However, the lab technician who recorded the blood type of the available blood units may have made an error. If the technician is 5% prone to making mistakes, can you conclude that Mr. R's chances of getting the right blood type are 99%?
1 Answer
📌 CONCEPT: Our intuition may lead us to assume that the probability of Mr. R getting the right blood type is indeed 99%, but we need to consider the role of the lab technician's error in this scenario.
📐 RULE / FORMULA: The probability of Mr. R getting the right blood type is not solely dependent on the accuracy of the blood bank's record, but also involves the probability of the lab technician making an error.
💡 WORKED EXAMPLE: If the lab technician has a 5% chance of making a mistake, and the blood bank's record is 99% accurate, the overall probability of Mr. R getting the right blood type is not 99%, but rather 99% * 95% = 94.05%.
⚠️ COMMON MISTAKE: Students often overlook the role of the lab technician's error and assume that the probability of Mr. R getting the right blood type is solely dependent on the blood bank's accuracy.
08 Aug 26
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