# Elvis twin brother statistics problem

Elvis had a twin brother (who died at birth).

Historically, approximately $$1/125$$ of all births were fraternal twins and 1/300 were identical twins. The probability that Elvis was an identical twin is approximately . . .

I'm trying to understand how to apply Bayes Theorem. To try to solve this problem above, I tried to apply Bayes Theorem by plugging in values.

Let $$I$$ be: Being an identical twin

Let $$B$$ be: Having an identical twin brother

We want to calculate $$P(I|B)$$.

Using Bayes, $$P(I|B)=P(I)*P(B|I)/P(B)$$

$$P(I)=1/300$$

$$P(B|I)=1$$ because we know that Elvis is male, so the chance of having an twin brother if we assume Elvis is an identical twin is $$100\%$$

$$P(B)=?$$

How do I calculate what the chance of having an twin brother is generally? It seems like I can't apply Bayes theorem if I can't calculate this value.

• I agree that they should have given you some information on the gender distribution of fraternal twins. After all, if his twin was female we'd know the twins were non-identical, so saying "brother" is evidence for the twins being identical. I suppose you could simply assume that fraternal twins satisfy the simplest statistics ($50\%$ MF and $25\%$ each of $MM$ and $FF$) and that identical twins are $50\%$ each of $MM$ and $FF$, though I do not believe these assumptions are strictly accurate.
– lulu
May 19 '20 at 23:22

• probability of a child being an identical twin (and twin sibling being the same sex) is $$\frac1{300} \times 1$$
• probability of a child being a fraternal twin and twin sibling being the same sex is $$\frac1{125}\times \frac12$$
then the probability of a child being an identical twin given a twin sibling is the same sex is $$\frac{\frac1{300} \times 1}{\frac1{300} \times 1+\frac1{125}\times \frac12} =\frac{5}{11}$$
• @leontp587 yes - I have edited in a $\times 1$ for your point May 20 '20 at 0:10