my mother told me “you should call [your friend who's there] and ask him if he's all right”, and I answered “there are 10 million people in London, so the probability that he was involved is about 1 in 30,000, which is less than the probability that he would die naturally in...”; my mother called me heartless before I even finished the sentence.

Your math is right but your mother has the right interpretation of the situation. If your friend is dead, calling him does neither of you any good! This is a 29,999 out of 30,000 chance to earn brownie points.