SOLUTION: A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 43% of people have ty

First, from the post, I will briefly list what we have given:

        (a)  43% of people have type O blood;

        (b)  19% of people have Rh- factor;

    and
        (c)  45% of people have type O blood  --OR--  Rh- factor.



Now they ask their first question

    1) Find the probability that a person has both type O blood  --AND--  the Rh− factor.


In elementary probability theory, there is a basic formula

         P(A U B) = P(A) + P(B) - P(A ∩ B).    (1)


In wording form, it says that the probability to have at least one of two events, A and B, is equal 
to the sum of individual probabilities P(A) + P(B) minus the probability to have these two events simultaneously.


From the condition, we have GIVEN that P(type O blood) = 0.43;
                                        
                                       P(Rh- factor)   = 0.19;

                    and                P(type O blood --OR--  Rh- factor) = 0.45.

So, in our case, the event A is (to have type O blood);  the event B is (to have Rh- factor);
    and the event  (A U B)  is  (to have type O blood --OR-- Rh- factor).


So, based on (1), we write 

          0.45 = 0.43 + 0.19 - P(type O blood --AND--  Rh- factor)     (2)

From this equation, we get momentarily  

         P(type O blood --AND--  Rh- factor) = 0.43 + 0.19 - 0.45 = 0.17.


Thus we get the answer to the first question:  

         the probability that a person has both type O blood  --AND--  the Rh− factor is  0.17.


This part is COMPLETED.




Now let's consider their second question

    2)  Find the probability that a person does NOT have both type O blood and the Rh− factor.


It is simply the COMPLEMENTARY probability to that we found in n. 1) :

        the probability that a person does NOT have both type O blood and the Rh− factor is  1 - 0.17 = 0.83.


It is the answer to the second question.