23 August 2018

This week Thursday puzzle

Bill Hubbard, what can I say – 3 different airlines, 6 flights, 4 different cities this week. You know who to blame for one more puzzle đź™‚

Anybody who works out the answer, feel free to post the answer only in the Comment section. Send your logic as a personal message to me. Do not write your logic in the Comments section.

Now to the puzzle.

In a Polynesian island, girls are highly preferred as a child. This has led to a strange practice over the years among couples who are trying to have a baby. If they have a baby boy, they keep trying to have another baby in the hope that it will be a girl. If it is a baby girl though, they stop having any more babies. Of course, given any birth, the probability of having a baby boy or baby girl is half and half. So, they keep having more babies as long as they are all boys and stop moment they have a girl

As a result, there are couples who have one girl, couples who have one boy and one girl, couples who have two boys and one girl, couples who have three boys and one girl (and the girl is always the last baby they have) but no couple with two girls (or more).

Here is the question: Over a longer period of time, what is the likely ratio of boys and girls in the island?

Posted August 23, 2018 by Rajib Roy in category "Puzzles

1. By rajibroy (Post author) on

You are likely to see half boys and half girls.
The answer seems deceptive initially but actually makes total sense. The simplest way to think about it is the following – at any point of time, letâ€™s say there have been â€śnâ€ť births. Immaterial of Ramesh’s overcomplicating with questions around monogamy and all that, as long as the probability of a boy and girl is half and half for every birth, you are likely to land up with n/2 boys and n/2 girls for n births.

In our mental model it initially does not fit in because we think of couples with a lot of boys and then one girl and wonder how can it be half and half. The trick is in realizing that there are MANY MORE couples with just one child – a girl – than there will be couples with many boys before they have a girl.

Take the case of 64 couples.

32 of them have girls first and 32 have boys. So we have boys to girls count as 32 and 32.
Now the couples who had 32 boys keep trying and eventually we have 16 more boys and 16 more girls. So we have 48 boys and 48 girls.
Now the 16 couples who had a boy (in fact, now they have two boys) will keep trying. Resulting in 8 more boys and 8 more girls. So, now we have 56 boys and 56 girlsâ€¦.

The aggregate count of boys and girls keep remaining the same as the other!

Kenneth quoted the original statement in the question that is only sentence that matters. In fact, using the same logic, of you take Melania’s point of 1:07 boys to every 1:00 girls for every birth, we will still land up exactly the same ratio of boys and girls (assuming for every birth, the probability remains consistently 1:07 to 1:00 )

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