“Jack and Jill, which bag do you choose for a chance of winning ten thousand dollars,” hailed the cheerful game show host Dusty Farlone, “the blue bag with three gold and seven silver coins, or the red bag with four gold and three silver coins. What do you say?”
“Dusty, what were the conditions, again?” asked Jack.
“You can pick six coins out of the blue bag with ten coins, or you can pick six coins out of the red bag with seven coins, in both cases replacing the coin each time. Whichever bag you choose, if you manage to pick three gold coins, you will win ten thousand dollars plus all the coins in the bag, of course,” said Dusty Farlone, smoothing his slick hairdo.
“Our charming Marlene will bring you the bag you select so you can pick the six coins, and help you put them back into the bag again,” said Dusty Fallon, indicating the svelte Marlene. “You have a minute to decide while the music plays.”
Jack turned to Jill. “You took a course in probability theory. Which bag seems the most promising for winning the prize, Jill, the blue or the red one?”
“Hmm… good question,” said Jill, “quick, hand me your scientific calculator, Jack.”
Which bag would you say has the greatest probability of success for picking three gold coins and winning the game show prize of ten thousand dollars?