A whodunnit - Part 2
There has been a murder
Vilila was reading the local newspaper when she noticed her son Wrinje staring at the front page, intently reading it.
Vilila: What are you reading?
Wrinje: It says there was a murder in the neighborhood.
Vilila: Yeah, I saw that. We saw the old lady walking in the park a few times - Ms. Glerna, I think her name was.
Wrinje: It says that her niece has been arrested for the murder. Did she do it?
Vilila: That’s very unlikely.
Wrinje: Why is it unlikely?
Vilila: What if your father was murdered and the police randomly chose somebody off the street and arrested them. Do you think it is likely that the person they picked murdered your father?
Wrinje: You talk about dad’s murder a lot.
Vilila: Answer the question.
Wrinje: No. Almost certainly not. Maybe they got very lucky. But, what does that have to do with the niece?
Vilila: The niece, Jansu, is also some random human. What are the odds that she did the murder?
Wrinje: Hmm... If you think of her as a random person, you are correct that she is unlikely to have killed the old lady Glerna. But, Jansu is a person known to the old lady. If we think of her in that way, it seems more likely that she did it.
Vilila: You are right! She definitely did it then.
Wrinje: You are insane! You jump from no chance to certainty in a second. Maybe we should think about it a little more.
Vilila: You better not use that type of language with me, or I will get you adopted by that murderous niece.
Wrinje: Okay. Calm down. Let’s think about it. I think you are right that the chance of it being Jansu goes up, given that she knows the victim. But, by how much?
Vilila: How am I supposed to know? Maybe we can talk about this with your cousin Glagalbagal. She is studying probability.
Wrinje: Good idea. Should I call her over for dinner?
Vilila: Do that. She likes eating raw limes, right? I’ll have to go buy some.
This discussion will continue in the next part when Glagalbagal joins Vilila and Wrinje. Before reading that, think about what Wrinje said given what you know about the world. Is it more likely that Jansu murdered Glerna than a random person did? Why? While thinking about this, consider two possible scenarios:
60% of murders are done by people who know the victim
5% of murders are done by people who know the victim
Are your conclusions in these two cases any different?