Ray's Wife Proves He's All Wet

May 31, 2004

RAY: This week's puzzler is from the realm of home repair and maintenance.

My wife and I have had a long-standing debate about drinking water. One result is that we now have an under-the-sink filter, and a little spigot on the sink that dispenses just drinking water.

TOM: I think that's bogus.

RAY: I do too. In fact, I think all those things that come through your tap, like the cyclospora, arsenic, fecal-coliform and mercury are probably good for you, and help build a nice strong immune system.

Anyway, the filter is kind of a pain in the neck to change, because it's underneath the sink, and it's got a big canister. So, I always avoid changing it.

She says to me one day, "The filter needs to be changed."

I say, "Well, how do you know? I turn it on, water comes out, it tastes good and it seems clean. I can't tell that there's anything wrong."

She says, "I know it needs to be changed. It's supposed to be changed every year, and it's been two years."

Still not convinced, I said, "Look, if it weren't working, no water would come out."

She responded, "I know it isn't working, because the water isn't cold anymore. That's the sign that the filter needs to be changed."

So, I reluctantly get under the counter, spend half an hour getting saturated, and put the new filter in. I open the spigot, and it works.

She says, "See? The water is colder!"

And that's my question is this: How is a new filter refrigerating the water?
RAY: The real question is if the test comes back positive what is the real probability that you actually have the bucolic plague?

Let's say that where you live there are a million people, and .1 percent, or a thousand people out of a million, have the disease.

If the 999,000 disease-free people are tested, the results will say that one percent of them, or 9,990 have the disease when, in fact, they don't.

TOM: They're misdiagnosed!

RAY: Correct. And of the thousand people who do have the disease, the test results will say that 99% of them, or 990 have the disease. So we have a total of 10,980 positive results.

But, we know that out of a million people, only a thousand people really do have the disease. So, the chance that you have Bucolic Plague if you test positive is about one in eleven, or less than 10%.

The moral of the story is this: You shouldn't lock yourself in the bathroom, unless you have some really good magazines. Do we have a winner?

TOM: Of course! The winner is Jean Gaska from Shelbyana, Kentucky. For having her answer selected at random from all the correct answers that we got, Jean gets a $26 dollar gift certificate to the Shameless Commerce Division of Cartalk.com, where she can choose from a wide array of fine quality Car Talk junk.

Get the Car Talk Newsletter