I have two probability questions in which I do not understand why a particular method works for one but not for the other.
First question: In a 52 card deck what are teh chances you draw a blackjack (that is, one card is an Ace, and your other card is either a king, queen, jack, or ten)?
Second question: Given two dice what is the probability that you roll 1 on both of them?
For the first question I did $$(4/52)(16/51) = .024$$
This was incorrect.
For the second problem I did $$(1/6)(1/6) = .02777$$ which was correct. Why is the first question off by $2x$ while the second one is just fine? What makes these problems inherently different?