Information Theory

So i'm facing this problem. It sais

A Tribe leader has 2 Children. Modern researches came up with 2 conclusions.

A) He had 1 Daughter and 1 Son

B) He had 1 Daughter and 1 elder Son

And the questions are What is the information we gain by the A) conclusion alone, What is the information we gain by the B) conclusion alone, And what is the information we gain if we have both A and B conclusions.

So at first i thought the Possible results of the first question was A=[DS,DD,SS] so the probability would be

$P(DS) = \frac{1}3$

and therefore the information should be

$H(A)=-log_2(P(DS))$

that would result to $\simeq 1.5849$ (i think)

And i'm stuck there. How should i proceed with the next problem?

• Your calculation has some problems. I think you should have $\mathbb{P}(DS) = 1/2$, while $\mathbb{P}(DD) = 1/4$ in your notation. These three events are not equiprobable. – Xiangxiang Xu Sep 9 '18 at 9:16
• Since there are two children, we can write them as AB, where A is the firstborn. So there are four possible events: {DD, DS, SD, SS}, and they are equiprobable. I guess now you may finish the rest part. – Xiangxiang Xu Sep 9 '18 at 9:20