The blood type distribution in the United States is type A 4

The blood type distribution in the United States is type A, 41%; type B, 9%; type AB, 4%; and type O, 46%. It is estimated that during World War II, several errors were made in typing blood. In fact, 4% of inductees with type O blood were listed as having type A; 88% of those with type A were correctly listed; 4% with type B blood were listed as type A; and 10% with type AB blood were listed as type A. A soldier was wounded and brought to surgery. He was listed as having type A blood. What is the probability that this is his true blood type?

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Solution

P(A & L) = 41% * 88%
P(B & L) = 9% * 4%
P(AB & L) = 4% * 10%
P(O & L) = 46% * 4%

since Pr is a ratio, any consistent units can be used,
P(A | L) = (41*88)/(41*88 + 9*4 + 4*10 + 46*4) = 0.9328 <-