Biology Probability

Biology Level 2

The photograph shows the last Russian emperor, Nicholas II, his wife Alexandra, his four daughters (Olga, Tatiana, Maria and Anastasia) and his son Alexei, who was hemophiliac.

Let $P = \dfrac{a}{b}$ , for coprime positive integers $a$ and $b$ , be the probability that only two of the couple's daughters carry the gene for hemophilia.

Evaluate $a+b$ .

The answer is 11.

1 solution

Guilherme Dela Corte
Dec 25, 2014

It is expected to know that hemophilia is a recessive sex-linked, X chromosome disorder. This means, straightforward, that Alexei is $X_aY$ , Nicholas is $X_AY$ and Alexandra is $X_AX_a$ .

Because Nicholas is a man and will always pass the gene $X_A$ to his daughters, none of them are hemophiliac. However, the second gene comes from Alexandra, which can send either $X_A$ or $X_a$ , on a $\frac{1}{2}$ chance for each one.

Mathematical reasoning leads to the fact that $P = \binom{4}{2} \cdot (\frac{1}{2})^2 \cdot (\frac{1}{2})^2$ , so $P = \dfrac{3}{8}$ and thus $a+b = \boxed{11.}$

PS: Any of you ever had this fun with Biology?

Biology Probability

The answer is 11.

1 solution

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