How to prove that this statistic is not sufficient? Problem.
Given $X_1,X_2,X_3$ a random sample from the Bernoulli distribution with success $\theta$, show that the statistic $T= X_1+2X_2+3X_3$ is not sufficient.
My attempt
When I try to apply the factorization criterion I don't see this function inside the likelihood so I guess $T$ is not sufficient. However, I feel unsure if this is the right proof... Could you give me a hint?

Thanks to the hints provided by @utobi in the comments of my post, I think I got the answer myself. The conditional probability of observing the sample 1,1,0, given the statistic $T=3$ is
$$
P_\theta(X_1=1,X_2=1,X_3=0|T=3) = \frac{P_\theta(X_1=1,X_2=1,X_3=0,T=3)}{P_\theta(T=3)}\\
= \theta.
$$
Since this probability does depend on $\theta$, $T$ is not sufficient.
