User:Martin Hogbin/MHP - Parade

The solution presented by vos Savant in Parade (vos Savant 1990b) shows the three possible arrangements of one car and two goats behind three doors and the result of staying or switching after initially picking door 1 in each case:


 * {| class="wikitable" style="margin:left; text-align: center;"

! behind door 1 || behind door 2 || behind door 3 || result if staying at door #1 || result if switching to the door offered
 * Car || Goat || Goat || Car || Goat
 * Goat || Car || Goat || Goat || Car
 * Goat || Goat || Car || Goat || Car
 * }
 * Goat || Goat || Car || Goat || Car
 * }
 * }

A player who stays with the initial choice wins in only one out of three of these equally likely possibilities, while a player who switches wins in two out of three. The probability of winning by staying with the initial choice is therefore 1/3, while the probability of winning by switching is 2/3.