Dice Probability Question

[mike1212]

I'm going through the problem's in Packel's The Mathmatics of Games and Gambling.

I'm having a problem with the following quesiton:

Compute the probability of 2 or more dice showing the same number of spots when 4 dice are rolled. Hint: first compute the probability of all 4 dice being different by looking at 4 successive independent trials.


















answer is 13/18

[donkeyradish]

Roll 1 die
Then roll another, the chance of it being different is 5/6
Roll another, the chance of it being diffrent is 4/6
Finally the 4th roll, the chance of it being different is 3/6

Multiply these odds together and you get 60/216 chance of all 4 being different

So there must be 156/216 alternative outcomes or 13/18

[mike1212]

thanks!