I’m reminded that good math questions are all around us. The last day for teachers was Wednesday June 23rd and on the 24th I was already on my first climbing trip of the season. While taking a break between climbs, I overheard a group having a conversation about Poison Ivy.
“…so you’re telling me that anything green with three leaves is Poison Ivy?” said boy #1.
“No, not every three leaved plant is Poison Ivy. The only way to really know is to rub it on your face and then wait and see what happens.” Said man #1 with a smirk.
“I heard you should rub it on your friends instead.” Laughed a second man.
“Um, but only 75% of people react to Poison Ivy, so that might not work.” Said a serious looking skinny boy walking behind the group.
“Then we’d just have to rub it on all four of us to see if we get itchty.” Said man #2 again.
The skinny boy then started to say “But you’d only have to rub it on one of us to see…” as they walked away down the carriage road
Ok, so let me start by saying that no one should rub anything on anyone. This is a terrible way to test if something is Poison Ivy, though I suppose it would work.
The interesting question is if we did have to test Poison Ivy, and only 75% of the population is affected, how many people would we have to attempt to infect before proving that it is or isn’t Poison Ivy?
1 person? 4 people? 10 people? 100 people?
Even if we tested 1,000 people and none of them became itchy, does that prove that the plant is not Poison Ivy?
This is also a good time to discuss theory and reality…though it may be possible to get lucky and not have anyone react, is it likely to happen? If 100 people in a row didn’t react to a particular plant, could you assume that it is safe?
“…so you’re telling me that anything green with three leaves is Poison Ivy?” said boy #1.
“No, not every three leaved plant is Poison Ivy. The only way to really know is to rub it on your face and then wait and see what happens.” Said man #1 with a smirk.
“I heard you should rub it on your friends instead.” Laughed a second man.
“Um, but only 75% of people react to Poison Ivy, so that might not work.” Said a serious looking skinny boy walking behind the group.
“Then we’d just have to rub it on all four of us to see if we get itchty.” Said man #2 again.
The skinny boy then started to say “But you’d only have to rub it on one of us to see…” as they walked away down the carriage road
Ok, so let me start by saying that no one should rub anything on anyone. This is a terrible way to test if something is Poison Ivy, though I suppose it would work.
The interesting question is if we did have to test Poison Ivy, and only 75% of the population is affected, how many people would we have to attempt to infect before proving that it is or isn’t Poison Ivy?
1 person? 4 people? 10 people? 100 people?
Even if we tested 1,000 people and none of them became itchy, does that prove that the plant is not Poison Ivy?
This is also a good time to discuss theory and reality…though it may be possible to get lucky and not have anyone react, is it likely to happen? If 100 people in a row didn’t react to a particular plant, could you assume that it is safe?