The blood type distribution in the United States is type A, 41%; type B, 9%; typ

Question

The blood type distribution in the United States is type A, 41%; type B, 9%; type AB. 4%; and type 0, 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? (YOU MUST USE BAYE?S RULE TO RECEIVE CREDIT FOR THIS ASSIGNMENT)

Explanation / Answer

First we must to calculate the initial probability in fractions, so we have:

Type A=0,41% ====>41/100
Type B=0,09% ====> 9/100
Type AB=0,04% ====>4/100
Type O=0,46% ====>46/100
Total =============>100/100

Then, we have that all the problem is concetrated in the type A and we have that the probability of this type is 41/100.

To calculate the percentage of blood type O that was listed as A we have to multiplicate the 4%=0.04=4/100 to the probability of A
(4/100)x(41/100)=0.0164

To calculate the percentage of blood type B that was listed as A we have to multiplicate the 4%=0.04=4/100 to the probability of A
(4/100)x(41/100)=0.0164

To calculate the percentage of blood type AB that was listed as A we have to multiplicate the 10%=0.10=10/100 to the probability of A
(10/100)x(41/100)=0.04

then we have that 88% of people listed as type A is right

(41/100)x(88/100)=0.3608

Then we must substract the previous probabilities to 0.3608

0.0164+0.0164+0.04=0.0728

0.3608-0.0728=0.288

We have 28% that this is the true blood type

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