3 January 2016

# A puzzle – seemingly simple, but not quite

Here you go Debajyoti – since you were clamoring for another one. This one involves probability and can be considered very simple or very intriguing depending on your point of view…

I was having drinks with two of my friends last evening when the discussion meandered around our kids. All three of us have two kids each and no twins. Chris mentioned that his boy has really taken to high school football. The other child is less inclined towards sports and prefers to excel academically. Rick, the other friend – who is the youngest of the three of us – talked about his four year old son overjoyed with his grandparents’ visit during Christmas and all the gifts he got. Rick and his wife also just had a baby – and that was one more reason the grandparents had come – to help them around in the house.

So, now the question for you: Which of my two friends – Chris or Rick is more likely to have a daughter?

Posted January 3, 2016 by Rajib Roy in category "Puzzles

28 COMMENTS :

1. By Rajib Roy on

I should have mentioned – this is a pure math problem. No trickery in English words or stereotypes like girls are (allegedly) not into sports or who kind of kid likes gifts etc etc

2. By Rajib Roy on

🙂 Unbelievably enough, Anastassia, when I was trying to formulate the problem, I thought of Chris’s son, so I put his name down. When I had to come with the next name, I thought about Chris’s old team members and came up with Rick. I thought about you too but it would be a difficult sell that you would be out drinking with us what with a new born and all that 🙂 On the other hand, want to go for a run this week? 🙂

1. By Anastassia Dees on

Would love to go for a run, but would need a rain check for this week – tweaked something in my foot during Saturday’s run (6 miles!), taking it easy this week.

2. By Rajib Roy on

I was slow though. The guy who came first had already reached home, had his lunch and was taking his afternoon siesta when I showed up at the finish line!! 🙂

3. By Madhusudhan M. Reddy on

Rick and his wife just had a ‘baby’. Is it a boy or a girl. Or, is it left unknown intentionally? Binomial coefficients come to mind.

4. By Rajib Roy on

Madhusudhan, if that was made explicit, there would be no question about the answer. It is purposely left open

5. By Madhusudhan M. Reddy on

May be I misunderstood the question, there are four kids in total now. I was under the impression, if either of them has another baby, to make the total to 5, what would be the probability that the 5th child is a girl.

6. By Rick Ward on

I’m going to say that Chris is more likely to have a daughter. Speaking from experience, if “Rick” had a newborn girl at home he would not be out having drinks with you! He would be home watching over her!

7. By Rajib Roy on

Ram and Madhusudhan, your answers are what most people would surmise. Hence the “seemingly simple part”. In mathematical terms though, probability theory will actually have a different answer!!

1. By Ram Narayanan on

oh. since I am in chennai, if I know the time and place of birth, maybe I can walk across to the friendly neighborhood astrologer in the street corner and ask what his answer is!

2. By Madhusudhan M. Reddy on

Given: B, ?, B, ? (Let’s say first two are Chris’ and the next two are Rick’s). The possibilities are:

B, B, B, B
B, G, B, B
B, B, B, G
B, G, B, G

So, I see the probability of either of them having a G is 2/4.

8. By Stephen Hunter on

Well, for me the answer is neither, the probability of either one of them giving birth to any child is zero. ” It isn’t that they cannot see the solution. It is that they cannot see the problem.”—GK Chesterton

9. By Somnath Daripa on

Rajib da, Chris, as the question says, ‘his boy has really taken to high school football’. The other cannot be a ‘boy’ as there is no qualifier to say ‘older, younger’.

10. By Rajib Roy on

In spite of my best effort I do not seem to be able to get to the math problem past my English words. Let me trying this Somnath and Dhananjay – “Chris and I were talking about one of his children – obviously a boy – who has taken to high school football. The other child, however, is less inclined towards sports and prefers to excel academically”. Again, don’t parse the English words. It is a math problem. (I do recognize that with improper English words, the math problem cannot be expressed adequately)

11. By Nitin Thakur on

I am going with Chris and here is why.

Here are the following combinations.

Chris’ First child – could be a boy or a girl

Chris’ second child – could be a boy or a girl

Rick’s second child could be a boy or a girl (its given that his first child is a boy)

If you break this up into multiple line items (one for each combination) you will find more combinations with Chris having a girl than with Rick having a girl.

This could be better explained using a pen and a paper.

12. By Rajib Roy on

No, I got your logic perfectly. And that is the answer. 2/3 probability for Chris and 1/2 for Rick

13. By Madhusudhan M. Reddy on

Ok, so, the possibilities are as follows, not knowing whether Chris’ first child is a boy or his second. We know Rick’s first child is a boy:

B, B, B, B
B, G, B, B
G, B, B, B
B, B, B, G
B, G, B, G
G, B, B, G

So, Chris having a G has a probability of 4/6 (2/3) while Rick has 3/6 (1/2).

14. By Rajib Roy on

SOLUTION:
By now, many of you figured out that the answer is not the seemingly simple 1/2 and 1/2. The trick is that we know Chris has a son that likes football but we do not know whether he has two sons and one of them likes football or a son and a daughter.
For Chris, the elder-younger combination can be B-B, B-G, G-B. It cannot be G-G since one of them is a boy. Now the probability that he has a daughter is 2/3.
For Rick though, the elder-younger combination can be B-G, B-B. Which means the probability of he having a daughter is 1/2.

BTE, whatever happened to Debajyoti? He asked for a puzzle and seemed to have gotten otherwise busy…

15. By Debajyoti Roy on

Rajib Roy … I was out of town and Facebook for the last 2 days. Looking at all the comments now and it is already solved. Good one! 🙂

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