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Four 12-sided dice are rolled. What is the probability that the number of dice showing a 2 is equal to the number of dice showing a 1? Express your answer as a common fraction. (Assume that the numbers on the 12 sides are the numbers from 1 to 12 expressed in decimal.)

 
 Sep 23, 2022
 #1
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P( no zero, no 1) = (10/12)^4

 

P(1 zero, 1 one, 2 others  different ones)  =   1/12 *  1/12  *  (10/12) *  (9/12) * 4!  

                                                                  =    (10*9*24) / (12*12*12*12)  =  180/  (12^3) = 15 / 144 

 

P(1 zero, 1 one, 2 others  that are the same as each other)  =   1/12 *  1/12  *  (10/12)  *1  *   4!/2!

                                                                                                =       10/(12^3) * 12

                                                                                                =      10/144

 

P(2zeros and 2 ones) =  (1/12)* (1/12) *   4!/(2!2!)  =   ( 1/144)  *6 =   6/144

 

Total  =   (15+10+6) / 144    =     31/144

 

You need to decide whether on not to accept this answer. 

 
 Sep 23, 2022

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