Question

Human blood is largely divided in to four blood groups (A, B, AB, and O) and also (separately) into             Rh-positive and Rh-negative. (There are also some very rare blood groupings, such as Mumbai, Lutheran, Kell, and Kipp.) This is very important in medicine, since a person may die or suffer serious harm if they receive a transfusion from an incompatible donor. According to the Stanford University School of Medicine Blood Center, the distribution of blood groups/types in the United States is as follows:
	Blood Group
	A	B	AB	0	Total
RH factor positive	714	170	68	748
RH factor negative	126	30	12	132
Total

Complete the table by filling in the “total” row and the “total” column.

Calculate P(blood group O)

Calculate P( Group O and Rh positive)

Calculate P( Group O or Rh-negative)

Calculate P( Group O and Rh-negative )

Calculate P( not group A)

Calculate P( Rh factor negative | group O )

Is being blood group O independent of being Rh factor negative?

Answer 1

	A	B	AB	O	Total
RH factor positive	714	170	68	748	1700
RH factor negative	126	30	12	132	300
Total	840	200	80	880	2000

(a)
P(blood group O) = 880/2000 = 0.44

(b)

P(Group O & Rh Positive) = 748/2000 = 0.374

(c)
P(Group O or Rh - negative) = P(Group O) + P(Rh - negative) - P(Group O & Rh - negative)

                                         = 880/2000 + 300/2000 - 132/2000

                                          = 0.44 + 0.15 - 0.066 = 0.524

(d)

P(Group O & Rh - negative) = 132/2000 = 0.066

(e)

P(not Group A) = 1- (840/2000) = 0.58

(f)
P(Rh factor ngative/ Group O) = P(Rh factor negative & Group O)/ P(Group O)

                                            = 132/880 = 0.15

(g)

P(blood group O & Rh factor negative) = 132/2000 = 0.066

P(blood group O) = 880/2000 = 0.44

P(Rh factor negative) = 300/2000 = 0.15

P(blood grup O) X P(Rh factor negative) = 0.44 X 0.15 = 0.066

We note that:
P(blood group O & Rh factor negative) = P(blood group O) X P(Rh factor negative)

So,

Answer is:

Yes. Blood group O is independent of bing Rh factor negative.