Well I know blond hair is recessive and brown/black hair is Heterozygous/Homozygous dominant, but what about red hair? Can a red hair mother and a brown hair father have offspring with blond, brown and red hair?
My blonde sister and her black-haired husband popped out two daughters: the first with blonde hair and the second with the most brilliant red hair you ever want to see.
The key? Strong Scottish ancestry on both sides of the family. Both branches of my family have Scottish blood (though moreso on my mother’s side), and I’ve had a redheaded female relative in each of the last four generations, but on alternating sides of the family tree. Maternal grandfather, paternal aunt, maternal cousin and now a niece. No redheaded male relatives that I know of, strangely enough.
Oh, wait, you’re asking about genetics. Um, I don’t know.
From here
So yes, a brown-haired father and red-haired mother could have offspring with brown, blonde, or red hair, depending on what the exact genetic makeup of the parents was.
Also:
Here’s one that has mystified me:
Can a man:
– with brown eyes and dark brown hair;
–whose brother has brown eyes and dark brown hair;
–and whose mother has brown hair and unknown eyes;
–and a father with unknown hair and eyes;
and a woman with:
–brown hair and blue eyes;
–whose sister has red hair;
–parents unknown;
Produce a child with:
–red hair and blue eyes?
I’m sure it’s possible especially with some variables unknown, but it’s pretty unlikely, isn’t it??
Let’s look at the eyes first. Both the child and the mother have blue eyes, so no problem there. The father has brown and a family history of brown, but that tells us nothing about the presence of any recessive blue alelles. So yes, certainly, a blue eyed child is no problem.
Now, hair. The mother has a family history of red hair, so we know there’s a recessive allele kicking around, so it’s not too surprising on her side. Again, the father’s family is all dominant (though with such a small sample size, that’s not terribly significant), which tells us nothing about the possible presence of a recessive red-hair allele. So, yeah, again, no problem.
My Wifes sister has darker brown hair and blue eyes and her husband is greek/italian so he has really dark hair and dark brown eyes (so does his mother and his brothers and sisters). Their very first child, a girl, came out with the fairest skin, bright blue eyes and bright red hair so its for sure possible. It happened with them in almost the EXACT scenario you listed. His father was actually a red head and my wifes sister had a red headed grandma and aunts so it doesn run on both sides of their family but still possible.
If I recall correctly, ANY thing is possible in human genetics. It’s been said that red headedness is recessive, but at one snapshot in time 10 of my mother in law’s 13 grandchildren were red headed. Yet she was only 2 of 7 to be red headed in her birth family.
Another case is my little husband, as I fondly refer to him as. He’s six foot five, but there is nohistory on either side for such tall men two generations back, after that we don’t know.
Also I had a good friend in college whose parents were medium to dark complected black folk, with no light colored folks in near relation, who was so light she could pass for white.
Chalk it up to the gene pool, toss of the dice. To speak to the OP’s question, yes any and all of us are subject to any combination of hair/eye color/hair color/skin tone. It’s like the Cosmic Grab Bag. 
I kinda like it that way.
Red-haired, green-eyed man with dark brown-haired wife with light brown eyes checking in.
A. Everyone in my immediate family (mother, father, brother) had brown/dark brown hair and either blue (Mom and Brother) or green eyes (Dad). I had a lot of “where’d he get that red hair?” questions. Apparently, there was some among both my parents’ aunts/uncles, so it must’ve skipped a generation.
B. My wife’s immediate all has dark brown hair, Mom and Sister with blue eyes, Dad with light brown eyes.
C. My kids are young, so they are still a bit lighter in color, but it looks like two of them will have brown hair and blue eyes, the other brown hair and light brown eyes. No red hair in sight. Maybe the generation-skipping thing will continue and one of them will have a redheaded kid.
Anecdotal, of course.
My mom has reddish-blond hair, as do I. My dad has brown hair. My sibs are platinum blond. All have blue eyes.
My wife has dark brown hair, with green/brown eyes. Our daughter is blonde, with grey eyes.
They lied* to you in high school biology.
[sub]* simplified explanations so your hormone-addled brain could understand ;)[/sub]
Good point. Most of us learn only about traits controlled by single allele pairs which express themselves thru simple dominance. Not many of us are taught about incomplete dominance, co-dominance, or traits controlled by multiple genes. So we end up with people thinking things like “Black genes are dominant”. Just goes to show how a little bit of knowledge can be a dangerous thing. 
Another case I know of: Mother has very light blond hair, no trace of red or brown in it. Father has brilliant, vivid, flame-red hair. They have three children.
First child has light blond hair, just like the mother.
Second child has flaming red hair, just like the father.
Third child has very dark brown hair, almost black.
This is a family well-known to me, and I’m certain that all of the hair colors are natural.
One of two red-haired siblings checking in. My father’s mother had red hair, and my father’s beard had a reddish tint if it grew long enough (every other hair on him was black), but on my mother’s side of the family the closest (and only) red-haired relative was a second cousin.
Then there’s the British royal family. Prince Harry’s ginger tint is responsible for the persistent rumor that James Hewitt was his actual father (Harry was two before Hewitt even met Princess Diana). Fewer people question where Princess Beatrice (Fergie and Andrew’s eldest) got her auburn hair. Yet either BOTH Harry and Beatrice have dubious parentage, or there’s a red hair gene hiding in the House of Windsor. (In the case of the mothers, of course, the gene wasn’t hiding at all; Fergie is famously redhaired and Diana had a strong family history.)
As for where the Windsors got the gene, good question. The Tudors were often redhaired, but their genetic connection to the current family is tiny to nonexistent.
A cousin of mine, fair & ruddy, married a redheaded woman with almost no melanin in her complexion (named, ironically, Melaney). They have several kids, mostly redheaded. But one of the boys has dark hair like his paternal grandparents.
You never know.
Switched at birth, perhaps?
Well, not to anyone’s knowledge, at least.
Some more anectdotal stuffs:
My kids’ aunt has red hair, and blue eyes. She’s of medium height and somewhat “zaftig”. She married a man from Guam; an Islander, with squatty stocky body, black hair and black/dark brown eyes.
They had three kids.
No. 1 son: big heavy build, black hair, dark brown/black eyes.
No. 2 son: tall, slim, blond hair, green eyes.
Daughter: medium height, a little “zaftig”, bright red hair and blue eyes.
So different in fact that the brothers would fight on the school bus as to whether they were actually related or the milkman’s kid.
No. 1 son usually settled the affair. Last time I heard from him, he was a professional wrestler out of Memphis 
Aside from the anecdotal stuff, isn’t hair color a little too mutable to really follow the old gene square? I mean most people have hairs of several different colors that blend together into the color of “hair” they have. But even this is not standard at all. What some people will call “strawberry blonde” other people will say is red, and others will call just blonde.