Marilyn puts two Litters of Puppies in one Basket

Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."

In her Parade Magazine column of August 10, 1997, Marilyn claims that two males and two females is not the most likely distribution of gender in a litter of four puppies.

Sorry, Marilyn

Since you normally credit the submitter of each question, I have to assume that unsigned submissions are written by you. I hope that your intent in posing this question is to teach us something about probability, not to deliberately mislead us. In my opinion, the most reasonable interpretation of the question is "Are two males and two females the most likely possibility?" It's clear from your answer that you consider "Three puppies of the same sex and one puppy of the opposite sex" to be a single possibility. I believe most people would consider "three males and a female" to be one possibility, and "three females and a male" to be a second possibility. People who consider these to be a single possibility would agree with Marilyn.

Here are the actual numbers:

Assuming that each puppy is equally likely to be male or female, a litter with two males and two females is the single most likely combination, with a probability of 6/16. Three males and a female is less likely, with a probability of only 4/16. Three females and a male also has a probability of only 4/16. So each of the splits you've listed is less likely than the split listed in the original question. Only when combined do they become more likely, and I don't see anything in the original question that suggests such a combination. (Four males has a probability of only 1/16, as does four females.)

Thanks to Charlie Kluepfel <ChasKlu@aol.com>, Noah Morrison <drmorr@lancnews.infi.net>, and Dale Hoyt <dlhoyt@negia.net> for writing to point out Marilyn's error.

http://www.wiskit.com/marilyn/puppy.html last updated June 30, 1998 by herbw@wiskit.com