Answer: the expected value of the sum of the rolls is 12.5
Step-by-step explanation:
Given that
Caleb has 4 sided die, 6 sided die and 12 sided die
first we calculate the expected number of each of the dice
so Expected number for 4 sided die will be;
E(X1)4-sided = ( (1+2+3+4) / 4 ) = 2.5
E(X2)6-sided = ( (1+2+3+4+5+6) / 6 ) = 3.5
E(X3)12-sided = ( (1+2+3+4+5+6+7+8+9+10+11+12) / 12 ) = 6.5
so, the expected value of the sum of the roll will be
E(X) = ( E(X1) + E(X2) + E(X3)
E(X) = 2.5 + 3.5 + 6.5
E(X) = 12.5
Therefore, the expected value of the sum of the rolls is 12.5
