The near-perfect match between Mr. Worrell's DNA and the sample recovered from the Manhattan victim's underwear means that the odds that he is the assailant are more than a trillion to one...
Wouldn't that make Worrell the least likely suspect?
UPDATE: Now, based on the discussion in the comments, I'm thinking I'm wrong. Or the odds that I'm wrong are... high.
ANOTHER UPDATE: A "trained probabilist" has arrived in the comments and is defending my original post, making odds of my being right higher. Or at least different.
MORE: Let me make an updated copy-editing point. Statistics should be stated in a very clear way that doesn't cause readers to stop and puzzle about which way the numbers work. So they could have written, for example: "There is only a one in a trillion chance that he is not the assailant."
By the way, does this statistic bother you because one trillion is far MORE that the total number of human beings who have ever lived? [Sorry, I had "less" there for a while-- and, me, talking about copy-editing....]
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6 comments:
I understand what they think they are doing, which is why they need the word "not" in there.
I'm no language expert, but I've got to agree with sp0t. As it reads, the odds of the guy being the assailant are a trillion times as likely as the guy not being a rapist.
Ann, if you put a not in there, you'd have to also use the full wording with "against", as sp0t indicated, which would lead to the double negative:
"The odds against the man not being the assailant are a trillion to one." Literally true, but awkward.
Dave: I'm very interested in this sort of thing too. I highly recommend the book "A Mathematician Reads the Newspaper."
Sp0t, stephen: I see your point. It read completely wrong to me, but when I thought about it again, I found it puzzling. As you note, the "odds against" or the "odds in favor." But I guess the "odds that" is the same as the "odds in favor." I think I need to take back what I wrote.
It does go against common usage. It would be better to say: "The odds the man is not the assailant are 1 in a trillion."
We usually talk about things in terms of how improbable they are, not how probable they are.
pmm: Are you SURE? Don't recall ever learning that in Prob & Stats, nor does a cursory internet search turn up any definition matching yours.
Besides, common usage trumps specialist usage when it comes to what should be printed an article intended for common people.
I think this wikipedia article states clearly common usage, going so far as to indicate that odds of 0.25 would equivalte to odds of 4:1 against as spoken by a British bookkeeper:
Wikipedia:Odds.
Doesn't all this show that it should have been written differently? Is there a standardized way to express odds? I'm no longer sure of what I thought I knew, which indicates to me that the form is not standardized enough to use in writing for laypersons.
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