Like father like son

7069 /www/nrich/html/content/id/7069/ 1 2011-07-08T14:43:24 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/7427">Warm-up</a></li> <li><a href="http://nrich.maths.org/6125">Try this next</a></li> <li><a href="http://nrich.maths.org/6680">Think higher</a></li> <li><a href="http://nrich.maths.org/7326">Read: mathematics</a></li> <li><a href="http://www.sciencemuseum.org.uk/educators/classroom_and_homework_resources/ks4/genetics.aspx">Read: science</a></li> <li><a href="http://en.wikipedia.org/wiki/Heredity">Explore further</a></li> </ul> Alice and Bob are happily married, and decide to have children. Alice is proud of her long blond hair and brown eyes. Bob is also happy with his brown eyes, which he inherited from his auburn father, although his mother was green - eyed. Alice knows that there is a small chance she might have a daughter looking like her (Alice's) mother, and that her daughter is much more likely to look like her. Bob, on the other hand, believes he won't have a son who reminds him (completely) of his father. 1. Can you determine the colour of Bob's hair? 2. Can you describe the eye colour of both Alice's parents? 3. How likely is it that Alice and Bob will have a blond son with green eyes? 4. How likely is it that they will have an auburn daughter? <div class="framework" style="text-align: justify;">Basic genetics: In the 19th century, a Czech monk, Gregor Mendel, experimented with pea plants. He noticed that plants were either tall or short, but when he crossbred a tall plant with a short one he didn't get a medium sized plant - he got a tall one. However, when he crossbred these new tall plants, sometimes it would result in a short one. He concluded that 'tall' was dominant and 'short' recessive. Experiments with true-bred green and yellow pea plants led him to conclude that each parent contributed either a G or a Y characteristic (gene), and that G is dominant over Y, so that GG, GY, and YG plants all appear green, and only YY plants appear yellow. He concluded that crossing a GG plant with a YY plant would result in offspring which all appeared to be green. However in the following generation, a GY or YG plant could give its offspring a Y gene rather than a G one. If the GY or YG plant was cross-bred with a YY plant, not all of the offspring would be green. For this problem, you may assume that the genes determining a person's hair and a person's eye colour are located in different chromosomes (so are independent of each other) and that the genes for green eyes and blond hair are recessive.</div></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">It is not envisaged that <a href="http://nrich.maths.org/7069">this problem</a> would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">By "completely" we mean a son which has both his grandfather's eyes and his hair. Based on this fact, can you now guess Bob's hair colour and genotype? How can Bob be absolutely sure that he can't have an auburn son? On the other hand, Alice has hopes having a daughter not looking like herself, but like her mother. But since Alice is brown - eyed, what does this mean about her mother? What can we conclude about the genotype of Alice?</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> 1. There is a chance that some of Alice and Bob's children will have brown eyes, since both Alice and Bob are brown - eyed. However, there is no chance that a child of them will look like Bob's father, so this means that no child of Alice and Bob can have brown hair. As Alice has blond hair herself, it means that Bob also must have blond hair (else he would have a dominant allele for brown hair, which could be transferred to produce an auburn offspring). Therefore, Bob is blond. 2. Bob has blond hair and brown eyes, but his mother was green - eyed, so he must have inherited a recessive green - eye allele from her. So, if we denote by H the (dominant) allele for brown hair, by h the (recessive) allele for blond hair, by E the (dominant) allele for brown eyes and by e the (recessive) allele for green eyes, we conclude the following. Bob's genotype is hhEe (because he has blond hair, and brown eyes, but has inherited an allele for green eyes from his mother). Alice knows for sure that her daughter will be blond. So, the fact that Alice knows there is a small chance her daughter might look like her mother is only related to her daughter's eyes. And since there is only a small chance that the daughter will have her grandmother's eyes means that the grandmother had green eyes, and so Alice also has genotype hhEe. So, she definitely inherited the brown eyes allele from her father. Therefore, Alice's father has brown eyes, and Alice's mother has green eyes. 3. Since both Alice and Bob have genotype hhEe, they can have a blond son with green eyes with probability $\frac{1}{8}$ (since there is a probability of $\frac{1}{4}$ of having a child with green eyes, and a probability of $\frac{1}{2}$ of the child actually being a boy. 4. Since both Alice and Bob are blond, they can never have auburn children, since they don't have the required allele. So the probability of them having an auburn daughter is zero. </mdoxml> 2 4 0 0 0 1 0 Like father like son What is the chance I will have a son who looks like me? Applications STEM - living world Probability Theoretical probability Probability Tree diagrams Admin No Teachers Notes