So a crime happens. Let’s say a bank robbery. There is video evidence that the robber is male, has red hair, is 6 foot 11, and is left handed.
The police go out and nab a 6 foot 11 left handed redhead.
Say that 2% of the area population are redheaded
Say that 10% are left handed
Say that 1% are 6 foot 11
So the case comes to court and the prosecutor grabs a friendly statistician, and says to the statistician…
“What are the odds that an innocent person would be left handed, 6 foot 11 and have red hair?”
The statistician does the sums, and says “0.002%.”
“That chance is tiny”, think the jury, “the guy must be guilty.”
Here’s the thing, there are half a million people who live in the city, 0.002% of 500,000 is 10, so there are likely to be about 10 people in the city who are redheaded, left handed, and 6 foot 11 inches.
The question an honest prosecutor would ask is “Given that the defendant has red hair, is 6 foot 11, and left handed, what are the odds he is guilty?”
To which the answer is “about 1 in 10.”