SOLUTION: During one month, a blood donation center found that 45.3% of the donors had the A antigen. 14.7% of the donors had the B antigen. 4.7% of the donors had the A antigen and the B

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Question 1131618: During one month, a blood donation center found that
45.3% of the donors had the A antigen.
14.7% of the donors had the B antigen.
4.7% of the donors had the A antigen and the B antigen.
84.3% of the donors were Rh+.
87.5% of the donors had the B antigen or were Rh+.
(a)
Find the percent of donors that have the A antigen or the B antigen.
(b)
Find the percent of donors that have the B antigen and are Rh+.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!

45.3% of the donors had the A antigen.
14.7% of the donors had the B antigen.
4.7% of the donors had the A antigen and the B antigen.
84.3% of the donors were Rh+.
87.5% of the donors had the B antigen or were Rh+.

a. P(have the A antigen or the B antigen) = %
-------------------
b P(have the B antigen and are Rh+) = P(B+)+P(Rh+)-P(B+ or Rh+)
= %

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

(a)   Find the percent of donors that have the A antigen or the B antigen.

The basic equality is P(A or B) = P(A) + P(B) - P(A and B), which gives P(A or B) = 45.3% + 14.7% - 4.7% = 55.3%. ANSWER

(b)   Find the percent of donors that have the B antigen and are Rh+.

The basic equality is P(B or Rh+) = P(B) + P(Rh+) - P(B and Rh+), which implies P(B and Rh+) = P(B) + P(Rh+) - P(B or Rh+), or P(B and Rh+) = 14.7% + 84.3% - 87.5% = 11.5%. ANSWER

The lesson to learn from my post is THIS

basic equality for probability is P(A or B) = P(A) + P(B) - P(A and B). It is true for any sets of events " A " and " B " inside the universal set of events.