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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?

Thank you

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up vote 5 down vote accepted

In short, order matters. In the first question, you calculated the probability that the first card you draw is an ace, and then the second card you draw is a king, queen, jack or ten. But you could also get blackjack by drawing the king/queen/jack/ten first, and then the Ace.

In the second question, the first factor represents the probability that the first die you roll is a 1, and the second factor represents the other die. If I asked you "what is the probability that you roll a 3?" the answer would be different from "what is the probability that you roll first a 1 and then a 2?" since you could also roll a 2 first and then a 1.

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