The Mysteries of Blood Type—Beyond the Textbook “A, B, and O”

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“Two parents with type A blood will have a child with type A blood.”

“Two parents with type O blood can only have a child with type O blood.”

“A type AB parent and a type O parent cannot have a child with type AB or type O blood.”

Many people probably remember being taught blood type inheritance this way.

However, the first statement is incorrect as written.Two type A parents can quite ordinarily have a type O child.

The third statement is also correct as long as we consider only ordinary ABO blood group inheritance, but it is not an absolute biological law.cis-ABWhen we consider this unusual ABO allele, a parent with an AB-like phenotype and a type O parent may have a child with an O or AB-like phenotype. If we also consider the Bombay phenotype, even a parent who appears to have type O blood may have a type A or type B child. Both actual pedigrees and molecular genetics have confirmed that cis-AB can produce the seemingly contradictory inheritance of “an O child from an AB mother.”

So what exactly was the “inheritance of A, B, and O” that we learned at school?

In fact, rather than being simply wrong, it is a model that extracts only the main features from a complex reality.

Even this simple model alone reveals some very interesting things.

Moreover, when we broaden our perspective from individual parents and children to the population as a whole, behind the population proportions of types A, B, O, and AB there emerges an exceptionally elegant mathematical structure called Hardy–Weinberg equilibrium.

From the familiar subject of blood type, genetics, molecular biology, probability theory, and population genetics all connect in a single thread.

Table of Contents

Can two type A parents have a type O child?

When I was young, I pictured blood type inheritance something like this:

A + A = A
A + O = A
A + B = AB
B + O = B
O + O = O

I imagined that combining the parents’ blood types would determine the child’s blood type.

But this understanding cannot explain, for example, how two type A parents can have a type O child.

At first glance, we may wonder, “Can that really happen?” In fact, there is nothing mysterious about it.

The problem is that the label “type A” alone does not tell us the person’s ABO genotype.

In other words, the story was already not so simple at the initial “A + A = A” stage of our understanding.

“Type A” includes both AA and AO

What we ordinarily call “type A,” “type B,” and so on is the phenotype.

In the classical ABO inheritance model, the ABO locus is considered to have the principal alleles A, B, and O. In genetics these may be written Iᴬ, Iᴮ, and i instead, but for simplicity I will use A, B, and O here.

A person inherits one allele from the father and one from the mother.

The typical relationships between genotype and phenotype are therefore as follows.

Blood type (phenotype)	Typical genotype
Type A	AA or AO
Type B	BB or BO
Type O	OO
Type AB	AB

A and B are codominant, while typical O behaves as recessive to A or B.

Thus, knowing only that someone has type A blood does not tell us whether the person is AA or AO.

For example, suppose both the father and mother are AO.

Because the child receives one allele from each parent, the combinations are:

	Mother A	Mother O
Father A	AA	AO
Father O	AO	OO

Therefore,

AA：1/4
AO：1/2
OO：1/4

In terms of phenotype,

Type A: 3/4
Type O: 1/4

In other words, when two type A parents are both AO, the probability that their child will have type O blood is 1/4.

AO and BO can produce all four blood types

Let us look at another standard example found in older teaching materials.

If the father is AO and the mother is BO, the combinations the child can inherit are:

These are the four possibilities.

Thus, each with a probability of 1/4, they may have a child with blood type:

Type AB
Type A
Type B
Type O

Thinking in this way, even ordinary ABO inheritance gives us:

Parents’ phenotypes	Typical possible phenotypes of the child
A × A	A, O
A × O	A, O
A × B	A, B, AB, O
B × B	B, O
B × O	B, O
O × O	O
AB × O	A, B
AB × AB	A, B, AB

Up to this point, we have merely described the ABO inheritance taught at school a little more carefully.

But real biology does not end here.

What are A, B, and O in the first place?

So far I have written “A gene,” “B gene,” and “O gene,” but more precisely, one locus called ABO has numerous alleles, including A, B, and O.

The ABO gene is located on chromosome 9, and the principal type A and type B alleles encode glycosyltransferaseswith different specificities.

On the surface of red blood cells is the H antigen, the material from which the A and B antigens are made.

In type A, an A-specific glycosyltransferase adds N-acetylgalactosamine to the H antigen to create the A antigen; in type B, a B-specific glycosyltransferase adds galactose to create the B antigen.

In typical type O, no functional A- or B-specific glycosyltransferase is produced, so the H antigen remains unmodified. The molecular basis of the ABO gene was elucidated by Yamamoto and colleagues in 1990. The well-known O1 allele causes a frameshift through a single-base deletion, but not all O alleles have exactly the same mutation.

Thus, behind the symbols A, B, and O lies the molecular biology of:

gene → enzyme → glycan structure → antigen on the red blood cell surface

Once we understand this mechanism, we can also see why blood types that depart from the “textbook rules” exist.

“Type AB and type O cannot produce type AB or type O” is not absolute

The usual genotype of type AB is AB.

When this is paired with OO, the child inherits either:

A + O → AO
B + O → BO

Thus, ordinarily:

Type AB × type O → type A or type B

They do not have a type AB or type O child.

This is correct under the ordinary ABO inheritance model.

However, there is an exception called cis-AB.

cis-AB—A and B are inherited together

In ordinary type AB, the allele with A activity and the allele with B activity are on different homologous chromosomes.

In cis-AB, however, a single ABO allele contributes to the formation of both A and B antigens.

In other words, the A and B characteristics can be inherited together from one parent on a single chromosome.

For example, schematically, consider a person with the genotype

cis-AB / O

and a person with

O / O

. Their child may be:

cis-AB / O

O / O

Thus, although the details of the serological phenotype may not be identical to ordinary type AB, a pedigree can exist in which an AB-like parent and a type O parent have an AB-like or type O child, seemingly contrary to Mendelian inheritance.

Indeed, cis-AB was initially recognized through families that were difficult to explain by ordinary inheritance, such as “a type O child born to a type AB parent”; its molecular genetic mechanism was later elucidated.

This is one reason it is dangerous to look only at a textbook table and declare, “This parent–child relationship is impossible.”

The even more mysterious Bombay phenotype

Even more intriguing is the Bombay phenotype (Bombay type, Oₕ type).

As noted above, creating the A and B antigens requires the H antigen as their foundation.

Producing this H antigen on red blood cells requires a FUT1geneseparate from the ABO gene.

However, people in whom both copies of FUT1 are nonfunctional cannot produce the H antigen.

Without the H antigen, even a person whose ABO gene includes A or B cannot produce A or B antigens on the red blood cell surface.

Looking only at the A and B antigens on the red blood cells, the person therefore appears to have type O blood.

This is the Bombay phenotype. The H antigen is the precursor of the ABO antigens, and it is well established both serologically and molecularly that FUT1 deficiency can prevent even the A and B antigens from being expressed.

This produces a curious outcome.

Suppose, for example, that a person with the Bombay phenotype actually has the ABO genotype:

A / O

But for FUT1, the person has:

h / h

and therefore cannot produce the H antigen, so no A antigen appears on the person’s red blood cells.

Suppose this person has a child with someone who has ordinary type O blood, for example:

O / O、H / H

If the child receives A from the Bombay-phenotype parent, O from the ordinary type O parent, and also a functional H allele, the child will be:

A / O、H / h

The child can now produce the H antigen.

The A-specific glycosyltransferase can then function, and the A antigen appears on the red blood cells.

In other words:

apparently type O parent × ordinary type O parent → type A child

can occur.

If the Bombay-phenotype parent has a B allele, the same logic allows a type B child.

The rule that “two type O parents can only have a type O child” was also a rule within a model that assumes ordinary ABO inheritance and H-antigen expression.

Moreover, the Bombay phenotype is not merely a “rare type O.” Because people with the Bombay phenotype have anti-H antibodies, transfusion of ordinary type O red blood cells can cause a severe hemolytic transfusion reaction; the distinction is therefore essential in transfusion medicine.

Profound indeed…

Blood type is more than ABO

The term “blood type” itself has different meanings in everyday language and medicine.

When someone ordinarily says, “I have type A blood,” they mean the ABO blood group, but ABO is not the only red blood cell blood group system.

There are many others, including Rh, MNS, Kell, Duffy, and Kidd.

According to the official database of the International Society of Blood Transfusion (ISBT), August 2026there are currently 49 recognized blood group systems. The 49th, the JAMA system, was approved at the June 2026 ISBT Kuala Lumpur Congress and added in the database update dated August 1.

In the past, combinations of several blood groups and genetic markers in serum proteins, not ABO alone, were sometimes used to assess biological parentage.

However, blood type can basically be used to exclude parentage by showing that “this combination is impossible,” but its ability to prove positively that “this person is the father because the blood types are compatible” is limited.

Modern parentage testing primarily uses DNA profiling with numerous STRs (short tandem repeats) and other markers. The ABO genotype itself can serve as a genetic marker, but its discriminatory power differs greatly from that of STR analysis.

It is therefore dangerous in two ways to determine parentage from blood type alone.

Even in ordinary ABO inheritance, phenotype and genotype are not in a one-to-one relationship, and exceptions such as cis-AB and the Bombay phenotype also exist.

And behind blood type proportions lies mathematics

So far, we have discussed “individual inheritance”: how one person comes to have a particular blood type.

But when we broaden our perspective to the population as a whole, something even more interesting happens.

A teaching resource I referred to previously gave the following proportions for ABO blood types among Japanese people.

Blood type	Proportion
Type A	38.2%
Type O	30.5%
Type B	21.9%
Type AB	9.4%

These figures appeared in the teaching resource at the time. Because I cannot now confirm their source or survey date, 2026they should not be cited as accurate nationwide estimates for the entire Japanese population as of .

Here they are used solely as data from the mathematics teaching material of that time.

What is interesting is that these four numbers do not exist independently of one another.

Behind them is a very simple structure derived from probability theory.

It is the Hardy–Weinberg equilibrium.

Hardy–Weinberg equilibrium

1908In

, British mathematician G. H. Hardy and German physician Wilhelm Weinberg independently demonstrated the same relationship for the frequencies of Mendelian alleles in a population.

Hardy’s paper was only about 2 pages long, but the relationship later became one of the fundamental principles of population genetics.

For ABO, let the frequencies of the A, B, and O alleles be:

A = p
B = q
O = r

Naturally,

p + q + r = 1

Assume that paternally and maternally derived alleles combine randomly in the population according to these frequencies.

The probability of OO is then:

r × r = r²

For AA, it is:

p²

For BB:

q²

For AB, on the other hand, there is the case of:

A from the father and B from the mother

and the case of:

B from the father and A from the mother

Therefore,

pq + qp = 2pq

Similarly,

AO = 2pr
BO = 2qr

In summary:

Genotype	Expected frequency
AA	p²
AO	2pr
BB	q²
BO	2qr
OO	r²
AB	2pq

In terms of phenotype:

Blood type	Expected frequency
Type A	p² + 2pr
Type B	q² + 2qr
Type O	r²
Type AB	2pq

Here the square formula appears

Let us add all of these together.

p² + 2pr + q² + 2qr + r² + 2pq

Reordering the terms gives:

p² + q² + r² + 2pq + 2pr + 2qr

This expression looks familiar.

It is, of course,

(p + q + r)²

itself.

And because

p + q + r = 1

(p + q + r)² = 1² = 1

The probabilities of all genotypes duly add up to 1.

This may seem obvious, but the multiplication rule of probability and the formula for squaring a sum learned in middle school directly yield the distribution of genotypes in a population.

That is the truly elegant part.

But the really interesting part begins here.

Working backward from blood type proportions to allele proportions

Let us use the figures from the teaching resource once more.

Type A: 38.2%
Type O: 30.5%
Type B: 21.9%
Type AB: 9.4%

First, consider type O.

In the ordinary model, only OO has the type O phenotype, so:

r² = 0.305

Therefore,

r = √0.305 ≒ 0.552

Thus, the frequency of the O allele is about 55.2%.

Next, add the proportions of types A and O.

0.382 + 0.305 = 0.687

On the other hand,

Type A + type O
= (p² + 2pr) + r²
= p² + 2pr + r²
= (p + r)²

Therefore,

(p + r)² = 0.687

so,

p + r = √0.687 ≒ 0.829

We found above that

r ≒ 0.552

, so:

p ≒ 0.829 − 0.552
≒ 0.277

The A allele frequency is about 27.7%.

Finally,

p + q + r = 1

, so:

q = 1 − p − r
≒ 1 − 0.277 − 0.552
≒ 0.171

Thus, the allele frequencies estimated from these data are:

A: about 27.7%
B: about 17.1%
O: about 55.2%

Predicting data we did not use

The calculations so far primarily used the proportions of types A and O.

Now let us calculate the proportions of types B and AB from these A, B, and O allele frequencies.

For type B:

q² + 2qr

Substituting the values gives:

0.171² + 2 × 0.171 × 0.552
≒ 0.218

That is,

about 21.8%

In the original data, the type B proportion was 21.9%.

The difference is only about 0.1 percentage point.

Next, consider type AB.

The type AB proportion is:

2pq

so,

2 × 0.277 × 0.171
≒ 0.095

That is,

about 9.5%

The original data gave 9.4%.

Again, the figures are nearly identical.

Rather than simply memorizing the proportions of the four blood types, if we estimate the three underlying allele frequencies from some of those proportions, we can predict the remaining, unused data with considerable accuracy.

That is quite inspiring.

How do these results compare with actual genotype data from Japanese people?

There is something even more interesting.

2015A study published in 1,427 that determined ABO genotypes in

Japanese participants reported the following frequencies of the A, B, and O alleles:

A: 26.7%
B: 17.7%
O: 55.6%

The distribution of ABO genotypes observed in that study was also statistically consistent with Hardy–Weinberg equilibrium (p = 0.46).

The values calculated earlier from the phenotype proportions in the old teaching resource were:

A: 27.7%
B: 17.1%
O: 55.2%

These are different data, with different samples and survey periods, so they cannot be treated as identical.

Nevertheless, the values are quite close.

The simple formula truly reveals the population’s underlying genetic structure.

Conditions for Hardy–Weinberg equilibrium

The old teaching resource listed conditions for the Hardy–Weinberg principle such as:

the population is sufficiently large
there is little emigration or immigration
the genotype does not change the probability of survival
people mate irrespective of blood type

The general direction is not wrong.

In modern population genetics, however, it is better to organize these ideas somewhat more carefully.

At the core is random mating and random union of gametes with respect to the locus.

If the allele frequencies are p, q, and r, random combination produces genotype frequencies in the next generation of:

p²、q²、r²、2pq、2pr、2qr

These are the Hardy–Weinberg proportions.

For the allele frequencies themselves also to remain unchanged across generations, there must be no, or only negligible, change caused by:

natural selection
mutation
gene flow between populations
genetic drift

Thus, the explanation in the old resource that “Hardy–Weinberg applies well because Japan is a populous island nation” is somewhat too crude from a modern perspective.

Genetic drift exists in principle in any finite population, and real human populations also have geographic and historical population structure.

In actual genetics, therefore, rather than assuming that “Japanese people are in Hardy–Weinberg equilibrium,” researchers statistically test whether the observed genotype frequencies in a sample are consistent with the values expected under Hardy–Weinberg equilibrium. Tests of Hardy–Weinberg equilibrium remain widely used in population genetics and genomics.

What does it mean to say that “blood type proportions do not change across generations”?

This point is easily misunderstood.

Hardy–Weinberg equilibrium encompasses two ideas.

One is:

genotype frequencies can be calculated from given allele frequencies through random combination

The other is:

if no forces change the allele frequencies, those frequencies are preserved across generations

Thus, Hardy–Weinberg equilibrium does not mean:

“gene proportions in the real world never change.”

Rather, it is a baseline model asking:

what should happen if no factors change allele frequencies?

If the observed distribution departs from that baseline, it offers clues for considering questions such as:

Is there population structure?
Is mating nonrandom?
Is natural selection operating?
Is there gene flow or genetic drift?
Or is there simply a genotyping error?

It may be somewhat like beginning in physics with a “world without friction.”

It is not reality itself, but a baseline for considering how reality departs from it.

An exceptionally well-designed mathematics lesson

I first learned about explaining Hardy–Weinberg equilibrium through blood types from a lesson plan in “Mathematical Description in Science” by Mr. Fujiki, formerly an instructor in the middle-school mathematics department.

Looking at it again, it is an exceptionally well-designed mathematics lesson.

It begins with the familiar topic of blood types and enters the subject of inheritance.

From there,

A × B

brings in the multiplication rule of probability.

Counting the two possibilities AB and BA gives:

2AB

Adding all the genotypes then gives:

A² + B² + O² + 2AB + 2AO + 2BO

which becomes:

(A + B + O)² = 1

and reveals the formula for squaring a sum.

We then work backward from real data to find the unknown values A, B, and O, and finally predict the still-unused proportions of types B and AB.

In other words, one story contains the entire progression:

inheritance → probability → formula for squaring a sum → parameter estimation from real data → prediction of unused data

It demonstrates that probability is not merely about textbook dice and coins, but a powerful tool for explaining real-world data.

I think this is an excellent topic for an advanced middle-school lesson or an aside after high-school students learn the multiplication rule for independent events.

Of course, rigorously explaining Mendelian inheritance, meiosis, loci, alleles, phenotypes, genotypes, and everything else would turn it into a biology lesson in its own right.

For a mathematics class, it is probably just right to explain basic inheritance and then move on to the probability model.

Conclusion

It began with a simple question:

“Why can two type A parents have a type O child?”

Researching the question first leads to the point that:

blood type phenotype and genotype are not the same thing

Looking further, we learn that:

ABO alleles such as cis-AB exist and cannot be represented by the simple A, B, and O model taught at school

We then learn that:

expression of ABO antigens involves not only ABO but also the separate FUT1 gene and the H antigen, producing phenomena such as the Bombay phenotype

And when we broaden our perspective from individual inheritance to the population as a whole:

the probabilistic structure of Hardy–Weinberg equilibrium emerges behind the population distribution of blood types

“Type A,” “type B,” “type O,” and “type AB.”

Behind just these four familiar terms, molecular genetics, glycobiology, transfusion medicine, probability theory, and population genetics are all connected.

We began with the line learned at school:

“A + A = A”

and arrived at a remarkably expansive world.

Blood types really are profound.

References

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(2026-08-12revised)