The probability of being an HLA match might be a lot lower than 1⁄20,000. Say that half the potential 16,000,000 donors would renege on donating if they were called, so we actually have 8,000,000 available members. A 1 in 20,000 chance implies that the chance that a given patient has no matches would be (1−1/20,000)8,000,000=2×10−174, when in reality the chance of having a match (probably with a donor who is willing to donate?) is at least 0.01. Maybe 1 in 2 million is more reasonable?
The probability of being an HLA match might be a lot lower than 1⁄20,000. Say that half the potential 16,000,000 donors would renege on donating if they were called, so we actually have 8,000,000 available members. A 1 in 20,000 chance implies that the chance that a given patient has no matches would be (1−1/20,000)8,000,000=2×10−174, when in reality the chance of having a match (probably with a donor who is willing to donate?) is at least 0.01. Maybe 1 in 2 million is more reasonable?