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0 . 7 5 Clue
THE TRAIN IS MOVING AT 40 MILES PER HOUR. IMAGINE THAT A FRIEND IS WALKING WITH YOU. WHEN THE TRAIN WHISTLE BLOWS, YOU HEAD AWAY FROM THE TRAIN, HE HEADS TOWARD IT. WHEN HE REACHES SAFETY, YOU WILL BE 6/8 (OR 3/4)OF THE WAY ACROSS THE BRIDGE, AND THE TRAIN WILL HAVE JUST REACHED THE BRIDGE. FOR THE TRAIN TO CROSS 4/4 OF THE BRIDGE IN THE TIME YOU CROSS THE REMAINING 1/4, THE TRAIN MUST BE MOVING FOUR TIMES YOUR SPEED THE PROBABILITY OF THE ANTS COLLIDING IS 0.75. EACH ANT CAN MOVE IN 2 DIFFERENT DIRECTIONS. BECAUSE THERE ARE 3 ANTS, THIS MEANS THAT THERE ARE 23 (8) POSSIBLE WAYS THAT THE ANTS CAN MOVE. NOW, THERE WILL NEVER BE A COLLISION BETWEEN ANY OF THE ANTS IF THEY ARE ALL WALKING IN THE SAME DIRECTION. AND, THE ONLY TIME THEY WILL BE WALKING IN THE SAME DIRECTION IS IF THEY ARE ALL WALKING EITHER CLOCKWISE OR COUNTER-CLOCKWISE AROUND THE TRIANGLE. SO, THERE ARE ONLY TWO SCENARIOS IN WHICH A COLLISION WILL NOT HAPPEN BETWEEN THE ANTS. THIS MEANS THAT THERE ARE 6 SCENARIOS WHERE THE ANTS WILL COLLIDE. AND 6 OUT OF 8 POSSIBLE SCENARIOS, MEANS THAT THE PROBABILITY OF COLLISION IS 6/8, WHICH EQUALS 3/4 OR 0.75. THUS, THE PROBABILITY OF THE ANTS COLLIDING IS 0.75 7 EGGS. THE FIRST PERSON BOUGHT ONE HALF OF HIS EGGS PLUS ONE HALF AN EGG (3 1/2 + 1/2 = 4 EGGS) THIS LEFT HIM 3 EGGS. THE SECOND PERSON BOUGHT ONE-HALF OF HIS EGGS PLUS ONE HALF AN EGG, (1 1/2 + 1/2 = 2 EGGS) LEAVING THE MAN 1 EGG. THE LAST PERSON BOUGHT ONE-HALF OF HIS EGGS PLUS ONE-HALF AN EGG, (1/2 + 1/2 = 1 EGG) LEAVING NO EGGS THE OPTION TO PULL THE TRIGGER AGAIN WILL GIVE A HIGHER PROBABILITY OF NOT BEING SHOT. THE KEY HINT HERE IS THAT THE BULLETS WERE LOADED ADJACENT TO EACH OTHER. THERE ARE 4 WAYS TO ARRANGE THE REVOLVER WITH CONSECUTIVE BULLETS SO THAT THE FIRST SHOT IS BLANK. THESE ARE THE POSSIBLE SCENARIOS: (XBBXXX) (XXBBXX) (XXXBBX) (XXXXBB) THE OTHER TWO SCENARIOS WOULD HAVE MEANT YOU GOT SHOT ON THE FIRST ATTEMPT. (BBXXXX) OR (BXXXXB). NOW LOOK AT THE SECOND SLOT IN THE 4 POSSIBLE SCENARIOS ABOVE. THE ODDS OF GETTING SHOT ARE 1⁄4 OR 25% (ONLY THE FIRST SCENARIO WOULD GET YOU SHOT). BUT IF YOU RESPIN, THERE ARE 2 BULLETS REMAINING AND A TOTAL OF 6 SLOTS, WHICH GIVES A PROBABILITY OF 2⁄6 OR 33% OF BEING SHOT