An $n$-sided die has sides labeled with the numbers $1$ through $n,$ inclusive, and has an equal probability of

An $n$-sided die has sides labeled with the numbers $1$ through $n,$ inclusive, and has an equal probability of landing on any side when rolled. If the die is rolled twice, what is the probability of rolling $1$ both times?

(1) If the die is rolled twice, the probability that the two rolls are different is $80\%.$

(1) If the die is rolled twice, the probability that the two rolls are equal is $\dfrac78.$

Answer: A

Source: Manhattan GMAT

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