{"id":656,"date":"2021-07-23T15:36:20","date_gmt":"2021-07-23T15:36:20","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=656"},"modified":"2025-09-16T21:13:29","modified_gmt":"2025-09-16T21:13:29","slug":"the-left-handed-sister-problem","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2021\/07\/23\/the-left-handed-sister-problem\/","title":{"rendered":"The Left-Handed Sister Problem"},"content":{"rendered":"\n

Suppose you meet someone who looks like the brother of your friend Mary. You ask if he has a sister named Mary, and he says “Yes I do, but I don’t think I know you.”<\/p>\n\n\n\n

You remember that Mary has a sister who is left-handed, but you don’t remember her name. So you ask your new friend if he has another sister who is left-handed.<\/p>\n\n\n\n

If he does, how much evidence does that provide that he is the brother of your friend, rather than a random person who coincidentally has a sister named Mary and another sister who is left-handed? In other words, what is the Bayes factor of the left-handed sister?<\/p>\n\n\n\n

Let’s assume:<\/p>\n\n\n\n