Act One: Show this clip of the recent Price is Right program. What questions do your students have?
We were wondering what the chances are of 3 contestants in a row, each spinning $1.00, and earning $1,000 each.
Act Two: What info would be useful?
The contestants are lined up by their winnings from lowest to highest. The object of the game is to come as close to $1.00 as you can without going over $1.00. If a contestant spins over $1.00 they lose the game. Each player will take up to two spins of the wheel; the wheel must go all the way around at least one time or the contestant must spin again. After the first spin, the spinner can choose to either stay with what he/she landed on or spin again; on the second spin, whatever the contestant hits will be added to the first score, but if he/she went over $1.00, that contestant is eliminated from the game.
When all three contestants have taken their spins, the contestant closest to $1.00 wins and goes into the Showcase round. If the first two contestants go over, the last contestant automatically advances to the Showcase, but gets only one spin to see if they can get $1.00. If the game ends in a tie, the tied contestants play a Spin-Off game and they each get only one spin, and the highest number wins. If any of the tied contestants gets $1.00 in their Spin-Off spin, they still get a $1,000 cash bonus and a bonus spin. http://priceisright.wikia.com/wiki/Showcase_Showdown
What are the chances of this happening, of all three contestants hitting $1,000?
Extension: This game has been played about 8,000 times as of fall 2016 and this reportedly the first time this is ever happened. How often should this event mathematically happen?
CCSS: 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8, HSS.CP.B.9
For members we have an editable docx and solutions.