Gaussian Mixture and K-Means ?! a big challenge?

This is taken from Tom. Mitche Material as Old-Exam.

I think the (2) is true and not (3). Who can verify me?

Yet, if you are using - as explained in (2) - a different covariance matrix for each cluster, the probability for the datapoint x is higher to belong to the cluster with the higher $r_i$ (a bigger covariance matrix).