[Mailbag] What Do You Do with the Ideas You Used to Call “Mistakes”

Guillaume ParĂ©, in the very interesting comments of my last post where I
urged us to reconsider mistakes: I do agree with what is written, but I am
still w...
1 week ago
The answer is (3/4)^n.
ReplyDeleteThe only way that A can fail to be a subset of B is if there exists an element x that belongs to A but does not belong to B.
For each x, the probability is 1/2 that x belongs to A, and 1/2 that x does not belong to B. Since the events are independent, the probability is 1/4 that x belongs to A but not B.
The probability that this event does not occur for a given x is 1  1/4 = 3/4, and the probability that it never occurs for any x is (3/4)^n.