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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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1 Answer 1

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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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