Players initially have a 2/3 chance of picking a goat. Those who swap always get the opposite of their original choice, so those who swap have 2/3 chance of winning the car. Players who stick have a 1/3 chance of winning the car. The solution is based on the premise that the host knows which door hides the car and intentionally reveals a goat. If the player selected the door hiding the car (1/3), then both remaining doors hide goats and the host may choose either door at random, and switching doors loses in 1/3. On the other hand, if the player initially selected a door that hides a goat (a 2-in-3 chance), then the host’s choice is no longer at random, as he is forced to show the second goat only, and switching doors wins for sure in 2/3.
Tag Archives: Solutions
Solution: Derek was the culprit.
Looking at Brian’s statement if it was Charles, then Brian was lying in his first statement, which makes the second statement true. Which would mean that it was both Charles and Alan. So it can’t be Charles.
Which means Derek was lying in his first statement, which makes the second statement true. Therefore it can’t be Alan.
So Eric’s second statement must be false, meaning his first statement was true, therefore it was Derek.
1 = John played Mozart on the Violin
2 = Nick played Bach on the Piano
3 = Kate played Mozart on the Violin
4 = Mary played Bach on the Violin
5 = Larry played Vivaldi on the Piano