I have a question for my statistics class that reads: Calculate the probability of rolling 4 of a kind with a fair 4 sided die. Express this using group operator notation and as probabilities using mathematical operators.

I interpreted this to mean to calculate the probability of rolling a the same number 4 times using a 4 sided die.

I wrote the notation as: P(rolling the same number 4x) = (rolling a 1 and rolling a 1 and rolling a 1 and rolling a 1) OR (rolling a 2 and rolling a 2 and rolling a 2 and rolling a 2) OR (rolling a 3 and rolling a 3 and rolling a 3 and rolling a 3) or (rolling a 4 and rolling a 4 and rolling a 4 and rolling a 4)

P(Ai) = (X1=1 ^ X2= 1 ^ X3= 1 ^ X4= 1) V (X1=2 ^ X2= 2 ^ X3= 2 ^ X4= 2) V (X1=3 ^ X2= 3 ^ X3= 3 ^ X4= 3) V (X1=4 ^ X2= 4 ^ X3= 4 ^ X4= 4)

I wrote it with the mathematical format using sigma;i=14P(X1=i)j=14P(X1=j)k=14P(X1=k)l=14P(X1=l)

but when I calculate this probability I get (4*4)x(1/4) which gives me 1; (4^4)(1/4*1/4*1/4*1/4).

When I calculate by hand as an independent event, I get 4*(1/4^4) which gives me the answer of 4/256 or 0.015.

I have a feeling I should be using the mathematical format with because the events are not mutually exclusive but I am not sure.

I am not sure which mathematical format to use. Someone please help me understand.