In a game show, three identical doors conceal a car behind one and goats behind two. You pick Door 1. The host, who knows where the car is, opens Door 3 to reveal a goat. He then gives you the option to switch to Door 2. Mathematically, what is your probability of winning the car if you switch?
2/3 (or ~66.7%)
Your initial pick (Door 1) had a 1/3 chance of being correct. The remaining doors (2 and 3) held a combined 2/3 probability. When the host eliminates Door 3, that full 2/3 probability transfers to Door 2.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
More logic riddles
Four people need to cross a dark, fragile bridge at night with one flashlight. The bridge holds at most two people at a time, moving at the speed of the slower person, and someone must return the flashlight. Person A takes 1 minute, B takes 2 minutes, C takes 5 minutes, and D takes 10 minutes. What is the fastest total time to get everyone across?
A library shelf holds volumes 1 through 5 of an encyclopedia in numerical order from left to right. A careless clerk pulls out volume 3 and places it on the extreme right end. Then, volume 1 is swapped with volume 4. Finally, volume 2 is placed immediately to the left of volume 5. Which volume is now in the exact middle position (third from the left)?
Three neighbors—Bob, Alice, and Carol—live side-by-side in three houses in that exact order from left to right. One owns a cat, one a dog, and one a parrot. The cat owner lives immediately to the left of the parrot owner. The dog owner lives on an end house. Who owns which pet?
A master lock has a three-digit code. The sum of the first and second digits is 8. The sum of the second and third digits is 14. The sum of all three digits is 17. What is the code?
What has words, but never speaks; has a spine, but no bones; and can take you anywhere without moving an inch?
What common English word becomes much shorter, lighter, and smaller when you add two letters to the end of it?