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.)
+118608
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.
