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probability

Implausible Murder

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I’ve become a fan of NCIS. I watch an episode almost every night. I like it. (I’m currently on season 7, so don’t worry about reading any spoilers for a recent episode.) Every once in a while, however, they come up with a plot that is so full of holes, it should never have seen airtime.

Case in point, this episode, called Code of Conduct. At the end the episode it is revealed that the murder was committed by the victim’s step-daughter, a short, teen-aged girl. She planned the murder and intended to frame her step-mother. She bought duct tape and a garden hose using her step-mother’s credit card and used those items in a somewhat clumsy attempt to make the murder look like a suicide. All of that is fine as far as it goes, but there are lots of details that do not make sense.

If you are going to take the trouble to deliberately murder someone, you certainly aren’t going to leave anything to chance. Along with your planning and preparation—making sure you have an alibi, throwing suspicion on someone else—you certainly will not neglect to use a method that will guarantee your victim ends up dead.

Now, don’t get me wrong. I have nothing but admiration for the writers of crime dramas tasked with coming up with ever more innovative, even bizarre, ways of divorcing souls from bodies. Nevertheless, I can’t help thinking that one crucial criterion for a planned murder is this: Is the plan certain to succeed? Does it depend too much on chance?

In this episode we are asked to believe that this girl was smart enough to make a plan to make her step-father’s death look like a suicide. She bought the necessary supplies. Yet the means she actually used to kill him was to bring him a thermos of liquid nitrogen, telling him it was coffee. She apparently gave no thought to the possibility that he would pour it into a cup before drinking it or that he would simply look at it and wonder why it didn’t look like coffee or that he might take a tentative sip (thinking it was hot) instead of taking a fatal gulp. It’s not that I can’t imagine a Marine gulping down coffee without looking at it. It’s that I can’t imagine a murderer relying on that behavior to commit the murder.

But that’s not all.

The murderer was discovered because she drove her dad’s car and left the seat adjusted for her small body. She brought him the fatal drink, waited until he was dead, then manhandled his six-foot corpse into the car parked in the driveway, attached the garden hose to the exhaust pipe and threaded it through the window and plugged the holes with duct tape. She did all this in the driveway where everything she did would be visible from the street. In fact, there were kids next door throwing TP into a tree and laughing the way only teen boys laugh, and they were the ones who discovered the Marine’s body. Again, it’s not that I can’t imagine a teen girl having the chutzpah to put a corpse in a car where any passerby could see it. It’s that I can’t imagine that being part of a well-designed plan.

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Probability

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I heard a caller on a local radio station this evening say something in praise of her 17-year-old son. The host said, “You must have a good relationship with your son.”

“Well, I have three sons,” said the caller. “So I have a 33% chance of having a good relationship.”

Of course, this was a flippant remark not meant as a serious estimate of the probability of having a good relationship. But it got me to wondering about the issue.

Suppose relationships can be unequivocally classified as either good or bad, and that both are equally likely. Then the probability of a good relationship with one son is 50%. With three sons, the probability of at least one good relationship out of the three is 87.5%, much better than 33%. In fact, for the probability to be only 33% for at least one good relationship with three sons, the probability of a good relationship with one son would have to be about 12.5%.

Probability can be tricky.

Suppose you are on a jury in a murder trial. A key piece of evidence comes from an eyewitness who claims that he saw the accused getting into a yellow cab. In tests the witness reliably identifies yellow cabs as yellow 95% of the time. The other 5% he mistakes them for white. He also correctly identifies white cabs 80% of the time, but 20% of the time mistakes them for yellow. However, 90% of the city cabs are white, and 10% are yellow. What is the probability that the witness actually saw a yellow cab?

Suppose there are 1000 cabs in the city. 900 are white, and 100 are yellow. Of the 900 white cabs, the witness would correctly identify 720 as white and misidentify 180 as yellow. Likewise, he would correctly identify 95 of the yellow cabs as yellow and misidentify 5 as white. Therefore, he would identify 275 cabs as yellow of which 180 are really white. The probability that the cab was yellow is 95/275 = 35%. Despite the reliability of the witness, the actual number of cabs of each color makes the probability of a mistaken identification 65%. It could easily be enough for reasonable doubt.

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Presumed Intelligence

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Suppose you are walking along a beach and you come across these lines scrawled in the sand:

Our vegetable love would grow
Vaster than empires and more slow

What would you think?

  1. That you had received a message from God
  2. That some human had been musing on Andrew Marvell’s poetry
  3. That some random process of wind and sea and sand crabs had accidentally produced marks resembling words

Certainly, it is possible to believe any of these. Yet I think most people would assume that the lines had been written by some human agent.

Now suppose you investigated and found that no one had visited that stretch of beach for days. Suppose you were able to show beyond doubt that the lines could not have been written by a human being. Then what would you believe? If the lines had to have been written by a non-human agent, which is more likely: God or nature?

I confess I don’t know. As a theist, I’m not even sure that a distinction between the two is significant. (In other words, if I were able to witness the words being formed by wind and sea and sand crabs, I don’t think I would find it any less supernatural.) I think I would cling to the notion that a human agent must be involved. After all, why would God quote Marvell?

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