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# Human blood may contain either or both of two antigens, A ISBN: 9780073401331 38

## Solution for problem 18E Chapter 2.1

Statistics for Engineers and Scientists | 4th Edition

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Problem 18E

Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is called type A, blood that contains only the B antigen is called type B, blood that contains both antigens is called type AB, and blood that contains neither antigen is called type O. At a certain blood bank, 35% of the blood donors have type A blood, 10% have type B, and 5% have type AB.

a. What is the probability that a randomly chosen blood donor is type O?

b. A recipient with type A blood may safely receive blood from a donor whose blood does not contain the B antigen. What is the probability that a randomly chosen blood donor may donate to a recipient with type A blood?

Step-by-Step Solution:

Step 1 of 3:

It is given that the blood containing only the A antigen is called type A and probability of type A blood is 35%. That is P(A)=0.35.

Blood containing only the B antigen is called type B and probability of type B is 10%. That is P(B)=0.1.

Blood containing both A and B antigen is called type AB and probability of type AB is 5%.

That is P( AB)=0.05.

Blood containing neither antigen is called type O.

Step 2 of 3:

(a)

Here we have to find the probability that randomly chosen blood donor is type O.

That is we have to find P(O).

We know that the total probability is 1.That is P(A)+P(B)+P(AB)+P(O)=1

Thus,

P(O)=1-P(A)+P(B)+P(AB)

=1-(0.35+0.1+0.05)

=1-(0.50)

=0.5

Hence,probability that the randomly chosen blood is type O is 0.5.

Step 3 of 3

##### ISBN: 9780073401331

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