Silly puzzle I read..

Ringo · #1 10-16-2006, 10:43 AM

I read a puzzle over the weekend that said:

"If a dog has a 50/50 chance of giving birth to a male or female puppy, what is the most likely outcome for a dog with 4 puppies: 1 of one sex and three of the other, or two of each?"

The answer I read was that one and three were most likely, since there are more combinations of one and three than the two and two. I didn't give this much though until recently - surely there's more combinations of two and two - ie, MMFF, MFMF, FFMM, etc..?

I reckon it's a [censored] puzzle, unless I'm getting something wrong. I forget where I read it too which makes it more frustrating. Maybe I dreamt is.. haha.

JustBeginning · #2 10-16-2006, 10:47 AM

If the puzzle specified the sex of the one puppy, or three puppy, then 2 and 2 would be the answer. AS it doesn't there means it's a 8/16 chance of a 3 to 1, and a 6/16 chance of a 2 to 2. Write all the possiblities out if it helps.

Ringo · #3 10-16-2006, 10:50 AM

Isn't it similar to asking what's more likely when you flip a coin 4 times - 2 heads and two tails, or one of one type and three of the other?

I'm still confused!

JustBeginning · #4 10-16-2006, 10:56 AM

It's similar, but not the same. If the question was which would happen more often, 1 male and 3 females, 2 males and 2 females, 1 female and 3 males. Then the chances of each would be 4/16, 6/16 and 4/16 respectively. But this question combines the first and third option so that it will give 8/16. And therefore more than the second option.
Ask if you don't understand where the above figures come from.

Ringo · #5 10-16-2006, 11:07 AM

I get it now.. thanks a lot [img]/images/graemlins/smile.gif[/img]

If it asked "what's more likely - one male and three females - OR two of each", the answer would be two of each. But as it asks about one and three - without specifying, then that's more likely.

Thanks again!

AaronBrown · #6 10-16-2006, 09:10 PM

Here is another way to think about it.

Regardless of the sexes of the first three puppies, there's a 50/50 chance that the fourth puppy will make it 3-1. If the first three are 3-0, the fourth can the the opposite of the 3. If the first three are 2-1, the fourth can be the same as the 2.

But to get 2-2, the first three have to be 2-1, then there's a 50/50 chance the fourth puppy is the same as the 1. If the first three are 3-0, you can never get 2-2.

So half the time you get 3-1, and half of three-quarters of the time, you get 2-2.