For this specific case, you could try asking the analogous question with a higher probability value. E.g. “if you’ve got a one-in-two DNA match on a suspect, does that mean it’s one-in-two that you’ve got that dude’s DNA?”. Maybe you can have some graphic that’s meant to represent a several million people, with half of the folks colored as positive matches. When they say “no, it’s not one-in-two”, you can work your way up to the three million case by showing pictures displaying what the estimated amount of hits would be for a 1 to 3, 1 to 5, 1 to 10, 1 to 100, 1 to 1000 etc. case.
In general, try to use examples that are familiar from everyday life (and thus don’t feel like math). For the Bayes’ theorem introduction, you could try “a man comes to a doctor complaining about a headache. The doctor knows that both the flu and brain cancer can cause headaches. If you knew nothing else about the case, which one would you think was more likely?” Then, after they’ve (hopefully) said that the man is more likely to be suffering of a flu, you can mention that brain cancer is much more likely to cause a headache than a flu is, but because flu is so much more common, their answer was nevertheless the correct one.
Most car accidents occur close to people’s homes, not because it’s more dangerous close to home, but because people spend most of their driving time close to their homes.
Most pedestrians who get hit by cars get hit at crosswalks, not because it’s more dangerous at a crosswalk, but because most people cross at crosswalks.
Most women who get raped get raped by people they know, not because strangers are less dangerous than people they know, but because they spend more time around people they know.
For this specific case, you could try asking the analogous question with a higher probability value. E.g. “if you’ve got a one-in-two DNA match on a suspect, does that mean it’s one-in-two that you’ve got that dude’s DNA?”. Maybe you can have some graphic that’s meant to represent a several million people, with half of the folks colored as positive matches. When they say “no, it’s not one-in-two”, you can work your way up to the three million case by showing pictures displaying what the estimated amount of hits would be for a 1 to 3, 1 to 5, 1 to 10, 1 to 100, 1 to 1000 etc. case.
In general, try to use examples that are familiar from everyday life (and thus don’t feel like math). For the Bayes’ theorem introduction, you could try “a man comes to a doctor complaining about a headache. The doctor knows that both the flu and brain cancer can cause headaches. If you knew nothing else about the case, which one would you think was more likely?” Then, after they’ve (hopefully) said that the man is more likely to be suffering of a flu, you can mention that brain cancer is much more likely to cause a headache than a flu is, but because flu is so much more common, their answer was nevertheless the correct one.
Other good examples:
Most car accidents occur close to people’s homes, not because it’s more dangerous close to home, but because people spend most of their driving time close to their homes.
Most pedestrians who get hit by cars get hit at crosswalks, not because it’s more dangerous at a crosswalk, but because most people cross at crosswalks.
Most women who get raped get raped by people they know, not because strangers are less dangerous than people they know, but because they spend more time around people they know.