Dicing
A game is being played with 3 dice, a red die, a blue die and a green die. All are fair dice and they are all numbered with 1, 2, 3, 4, 5, 6 on their faces.
A machine thoroughly tosses the dice in a metal drum, then spits one die at a time onto the table.
A man has bet on the three dice showing a combined total of 10.
The first die to be spit out is a 1. Did the man's chances of winning increase, decrease or stay the same as before any of the dice were rolled?
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1 solution
Moderator note:
Great question! What is the range of outcomes in which the probability would decrease / increase?
How do we analyze the general problem?
Before the dice were rolled, the man had a chance of 27/216 = 1/8 of winning. After the 1 emerged, he needs the other two dice to show a 9. This has a chance of 4/36 = 1/9 of occurring.