Two dice, told at least one is a four

Question

You roll two fair dice out of sight. A friend peeks and tells you, truthfully, that at least one of the two dice shows a 4. Given that, what is the probability that both dice show a 4?

Accepted Answer

The trap here is answering 	frac16. That would be the answer to a different question, "one particular die is a 4, what about the other." The clue "at least one is a 4" is weaker and vaguer, so we must count carefully. Think of the two dice as ordered (first die, second die), giving 36 equally likely outcomes. Now list the outcomes that contain at least one 4: - First die is 4: (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), that is 6 outcomes. - Second die is 4: (1,4),(2,4),(3,4),(4,4),(5,4),(6,4), another 6 outcomes. But (4,4) is in both lists, so we counted it twice. The true number of outcomes with …

Two dice, told at least one is a four

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