If you give away seven cents, what is the probability of getting a $1.75 in return?
I told my after-school tutoring kids we were going to work on probability.Â I handed each of them a penny.Â As I pressed the penny into each student’s palm, I said, “Here.Â I want this quarter back when we are finished.”Â Each child looked at his or her penny and said, “Okay.”
A Title One (NCLB) inspector was in the room watching. Â She chuckled.Â “You just taught me something,” she said.Â “If this works, I’m changing jobs.”
I told the students to look a their pennies closely, then record in their notebooks the chance of flipping that penny into the air, and having it land heads up.Â All four of the fifth graders and one of the fourth graders wrote 50%.Â The other two fourth graders weren’t certain.Â With a little prompting they came to realize their coins only had two sides and, if tossed, would have to land on one or the other.Â They each wrote down “half.”
They all flipped their coins 100 times and tallied heads or tails, proving that indeed, their 50% predictions were very accurate.Â Â The next thing I did was hand each child a die and ask them make the same sort of prediction for the number five.Â They all figured out very quickly the odds would be one in six, of obtaining a five.Â I asked them to record in their journals which of the two games they thought would have the best odds in winning, and explain why.
After they settled to write, I said, “I need my quarters now.”Â They all tried to hand me the pennies. Â “No,”Â I shook my head and pulled my hand away.Â “You said you’d give me quarters.”
Andi’s eyes grew wide.Â “We did!” She exclaimed.
Bill handed me his penny again.Â “Here’s your quarter, Ms. A.”Â he said.
I said, “Bill, this is a penny.Â I want a quarter.”
He answered, “Your odds of getting one are zero out of seven.”
The inspector gave me an A+.